Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Biolinguistics or Physicolinguistics? Is The Third Factor Helpful Or Harmful In Explaining Language?

Noam Chomsky (2005) proposed that a ‘third factor’, consisting of general principles and natural laws, may explain core properties of language in a principled manner, minimizing the need for either genetic endowment or experience. But the focus on third-factor patterns in much recent bio-linguistic work is misguided for several reasons: First, ‘the’ third factor is a vague and disparate collection of unrelated components, useless as an analytical tool. Second, the vagueness of the third factor, together with the desire for principled explanations, too often leads to sweeping claims, such as syntax “coming for free, directly from physics”, that are unwarranted without a case-by-case causal analysis. Third, attention is diverted away from a proper causal analysis of language as a biological feature. The point with biolinguistics is to acknowledge the language faculty as a biological feature. The best way forward towards an understanding of language is to take the biology connection seriously, instead of dabbling with physics.