Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out on the citizen supercomputer Ibercivis. Upon dilution, the pure model’s first-order transition becomes of the second order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their random field Ising model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.

Critical behavior of the dilute antiferromagnet in a magnetic field

We study the critical behavior of the diluted antiferromagnet in a field with the tethered Monte Carlo formalism. We compute the critical exponents (including the elusive hyperscaling violations exponent θ). Our results provide a comprehensive description of the phase transition and clarify the inconsistencies between previous experimental and theoretical work. To do so, our method addresses the usual problems of numerical work (large tunneling barriers and self-averaging violations).

Static versus dynamic heterogeneities in the D=3 Edwards-Anderson-ising spin glass

We numerically study the aging properties of the dynamical heterogeneities in the Ising spin glass. We find that a phase transition takes place during the aging process. Statics-dynamics correspondence implies that systems of finite size in equilibrium have static heterogeneities that obey finite-size scaling, thus signaling an analogous phase transition in the thermodynamical limit. We compute the critical exponents and the transition point in the equilibrium setting, and use them to show that aging in dynamic heterogeneities can be described by a finite-time scaling ansatz, with potential implications for experimental work.

Critical behavior of three-dimensional disordered Potts models with many states

We study the 3D Disordered Potts Model with p = 5 and p = 6. Our numerical simulations (that severely slow down for increasing p) detect a very clear spin glass phase transition. We evaluate the critical exponents and the critical value of the temperature, and we use known results at lower p values to discuss how they evolve for increasing p. We do not find any sign of the presence of a transition to a ferromagnetic regime.

Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

Spin glass phase in the four-state three-dimensional Potts model

We perform numerical simulations, including parallel tempering, a four-state Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the critical temperature and the value of the critical exponents. Nevertheless, the extrapolation to infinite volume is hampered by strong scaling corrections. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the “random permutation” Potts glass.

Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions

By performing a high-statistics simulation of the D = 4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.