Spin glasses on the hypercube

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the nontrivial problem of generating these lattices. Afterward, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are the following: i the dynamics is ruled by an infinite number of time sectors, ii the aging dynamics consists of the growth of coherent domains with a nonvanishing surface-volume ratio, and iii the propagator in Fourier space follows the p4 law. We study as well the finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.

Critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions

We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulations and a finite-size scaling analysis. By using a field programmable gate array, we have been able to thermalize a large number of samples of systems with large volume. This has allowed us to observe a spin-glass ordered phase in d=4 and to study the critical properties of the transition. In d=3, our results are consistent with the presence of a Kosterlitz-Thouless transition, but also with different scenarios: transient effects due to a value of the lower critical dimension slightly below 3 could be very important.

Condensados de Bose-Einstein em redes óticas: a transição superfluido-isolante de Mott em redes hexagonais e a classe de universalidade superfluido-vidro de Bose em 3D

Estudamos transições de fases quânticas em gases bosônicos ultrafrios aprisionados em redes óticas. A física desses sistemas é capturada por um modelo do tipo Bose-Hubbard que, no caso de um sistema sem desordem, em que os átomos têm interação de curto alcance e o tunelamento é apenas entre sítios primeiros vizinhos, prevê a transição de fases quântica superfluido-isolante de Mott (SF-MI) quando a profundidade do potencial da rede ótica é variado. Num primeiro estudo, verificamos como o diagrama de fases dessa transição muda quando passamos de uma rede quadrada para uma hexagonal. Num segundo, investigamos como a desordem modifica essa transição. No estudo com rede hexagonal, apresentamos o diagrama de fases da transição SF-MI e uma estimativa para o ponto crítico do primeiro lobo de Mott. Esses resultados foram obtidos usando o algoritmo de Monte Carlo quântico denominado Worm. Comparamos nossos resultados com os obtidos a partir de uma aproximação de campo médio e com os de um sistema com uma rede ótica quadrada. Ao introduzir desordem no sistema, uma nova fase emerge no diagrama de fases do estado fundamental intermediando a fase superfluida e a isolante de Mott. Essa nova fase é conhecida como vidro de Bose (BG) e a transição de fases quântica SF-BG que ocorre nesse sistema gerou muitas controvérsias desde seus primeiros estudos iniciados no fim dos anos 80. Apesar dos avanços em direção ao entendimento completo desta transição, a caracterização básica das suas propriedades críticas ainda é debatida. O que motivou nosso estudo, foi a publicação de resultados experimentais e numéricos em sistemas tridimensionais [Yu et al. Nature 489, 379 (2012), Yu et al. PRB 86, 134421 (2012)] que violam a lei de escala $\\phi= u z$, em que $\\phi$ é o expoente da temperatura crítica, $z$ é o expoente crítico dinâmico e $ u$ é o expoente do comprimento de correlação. Abordamos essa controvérsia numericamente fazendo uma análise de escalonamento finito usando o algoritmo Worm nas suas versões quântica e clássica. Nossos resultados demonstram que trabalhos anteriores sobre a dependência da temperatura de transição superfluido-líquido normal com o potencial químico (ou campo magnético, em sistemas de spin), $T_c \\propto (\\mu-\\mu_c)^\\phi$, estavam equivocados na interpretação de um comportamento transiente na aproximação da região crítica genuína. Quando os parâmetros do modelo são modificados de maneira a ampliar a região crítica quântica, simulações com ambos os modelos clássico e quântico revelam que a lei de escala $\\phi= u z$ [com $\\phi=2.7(2)$, $z=3$ e $ u = 0.88(5)$] é válida. Também estimamos o expoente crítico do parâmetro de ordem, encontrando $\\beta=1.5(2)$.

First-order transition in a three-dimensional disordered system

We present the first detailed numerical study in three dimensions of a first-order phase transition that remains first order in the presence of quenched disorder (specifically, the ferromagnetic-paramagnetic transition of the site-diluted four states Potts model). A tricritical point, which lies surprisingly near the pure-system limit and is studied by means of finite-size scaling, separates the first-order and second-order parts of the critical line. This investigation has been made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that plague the standard approach. Entropy, rather than free energy, is the basic object in this approach that exploits a recently introduced microcanonical Monte Carlo method.

First Order Phase Transition in a 3D disordered system

We present a detailed numerical study on the effects of adding quenched impurities to a three dimensional system which in the pure case undergoes a strong first order phase transition (specifically, the ferromagnetic/paramagnetic transition of the site-diluted four states Potts model). We can state that the transition remains first-order in the presence of quenched disorder (a small amount of it) but it turns out to be second order as more impurities are added. A tricritical point, which is studied by means of Finite-Size Scaling, separates the first-order and second-order parts of the critical line. The results were made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that arise using the standard methodology. We also made use of a recently proposed microcanonical Monte Carlo method in which entropy, instead of free energy, is the basic quantity.

The thermodynamics and statistical mechanics of protein folding

The physics of self-organization and complexity is manifested on a variety of biological scales, from large ecosystems to the molecular level. Protein molecules exhibit characteristics of complex systems in terms of their structure, dynamics, and function. Proteins have the extraordinary ability to fold to a specific functional three-dimensional shape, starting from a random coil, in a biologically relevant time. How they accomplish this is one of the secrets of life. In this work, theoretical research into understanding this remarkable behavior is discussed. Thermodynamic and statistical mechanical tools are used in order to investigate the protein folding dynamics and stability. Theoretical analyses of the results from computer simulation of the dynamics of a four-helix bundle show that the excluded volume entropic effects are very important in protein dynamics and crucial for protein stability. The dramatic effects of changing the size of sidechains imply that a strategic placement of amino acid residues with a particular size may be an important consideration in protein engineering. Another investigation deals with modeling protein structural transitions as a phase transition. Using finite size scaling theory, the nature of unfolding transition of a four-helix bundle protein was investigated and critical exponents for the transition were calculated for various hydrophobic strengths in the core. It is found that the order of the transition changes from first to higher order as the strength of the hydrophobic interaction in the core region is significantly increased. Finally, a detailed kinetic and thermodynamic analysis was carried out in a model two-helix bundle. The connection between the structural free-energy landscape and folding kinetics was quantified. I show how simple protein engineering, by changing the hydropathy of a small number of amino acids, can enhance protein folding by significantly changing the free energy landscape so that kinetic traps are removed. The results have general applicability in protein engineering as well as understanding the underlying physical mechanisms of protein folding. ^

Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

Phase diagram of the bosonic double-exchange model

The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic (AFM) superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

Dynamical generation of a gauge symmetry in the double-exchange model

It is shown that a bosonic formulation of the double-exchange model, one of the classical models for magnetism, generates dynamically a gauge-invariant phase in a finite region of the phase diagram. We use analytical methods, Monte Carlo simulations and finite-size scaling analysis. We study the transition line between that region and the paramagnetic phase. The numerical results show that this transition line belongs to the universality class of the antiferromagnetic RP^(2) model. The fact that one can define a universality class for the antiferromagnetic RP^(2) model, different from the one of the O(N) models, is puzzling and somehow contradicts naive expectations about universality.

Universal critical behavior of the two-dimensional Ising spin glass

We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.

Application of lateral photovoltage towards contactless light beam induced current measurements and its dependence on the finite beam size

The nature of the signal due to light beam induced current (LBIC) at the remote contacts is verified as a lateral photovoltage for non-uniformly illuminated planar p-n junction devices; simulation and experimental results are presented. The limitations imposed by the ohmic contacts are successfully overcome by the introduction of capacitively coupled remote contacts, which yield similar results without any significant loss in the estimated material and device parameters. It is observed that the LBIC measurements introduce artefacts such as shift in peak position with increasing laser power. Simulation of LBIC signal as a function of characteristic length L-c of photo-generated carriers and for different beam diameters has resulted in the observed peak shifts, thus attributed to the finite size of the beam. Further, the idea of capacitively coupled contacts has been extended to contactless measurements using pressure contacts with an oxidized aluminium electrodes. This technique avoids the contagious sample processing steps, which may introduce unintentional defects and contaminants into the material and devices under observation. Thus, we present here, the remote contact LBIC as a practically non-destructive tool in the evaluation of device parameters and welcome its use during fabrication steps. (C) 2014 AIP Publishing LLC.

Dynamic scaling of bred vectors in spatially extended chaotic systems

We unfold a profound relationship between the dynamics of finite-size perturbations in spatially extended chaotic systems and the universality class of Kardar-Parisi-Zhang (KPZ). We show how this relationship can be exploited to obtain a complete theoretical description of the bred vectors dynamics. The existence of characteristic length/time scales, the spatial extent of spatial correlations and how to time it, and the role of the breeding amplitude are all analyzed in the light of our theory. Implications to weather forecasting based on ensembles of initial conditions are also discussed.

Semiclassical scaling functions of sine-Gordon model

We present an analytic study of the finite size effects in sine-Gordon model, based on the semi-classical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi-periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the sine-Gordon model on the cylinder. (C) 2004 Elsevier B.V. All rights reserved.

Modeling Finite Buffer Effects on TCP Traffic over an IEEE 802.11 Infrastructure WLAN

The network scenario is that of an infrastructure IEEE 802.11 WLAN with a single AP with which several stations (STAs) are associated. The AP has a finite size buffer for storing packets. In this scenario, we consider TCP controlled upload and download file transfers between the STAs and a server on the wireline LAN (e.g., 100 Mbps Ethernet) to which the AP is connected. In such a situation, it is known (see, for example, (3), [9]) that because of packet loss due to finite buffers at the Ap, upload file transfers obtain larger throughputs than download transfers. We provide an analytical model for estimating the upload and download throughputs as a function of the buffer size at the AP. We provide models for the undelayed and delayed ACK cases for a TCP that performs loss recovery only by timeout, and also for TCP Reno.

Modeling finite buffer effects on TCP traffic over an IEEE 802.11 infrastructure WLAN

The network scenario is that of an infrastructure IEEE 802.11 WLAN with a single AP with which several stations (STAs) are associated. The AP has a finite size buffer for storing packets. In this scenario, we consider TCP-controlled upload and download file transfers between the STAs and a server on the wireline LAN (e.g., 100 Mbps Ethernet) to which the AP is connected. In such a situation, it is well known that because of packet losses due to finite buffers at the AP, upload file transfers obtain larger throughputs than download transfers. We provide an analytical model for estimating the upload and download throughputs as a function of the buffer size at the AP. We provide models for the undelayed and delayed ACK cases for a TCP that performs loss recovery only by timeout, and also for TCP Reno. The models are validated incomparison with NS2 simulations.