Extended Universality in Potts Models on Square and Triangular Lattices

Joan Adler, Ian Graham Enting, Vladimir Privman A

The authors present a study of an extended (35-power) low-temperature series for the susceptibility of the ordinary two-site three-state Potts model on the square lattice as well as reanalyses of several extant series for the three-site three-state Potts model on the triangular lattice. Dominant and confluent singularities are investigated and the exponents of both are found to be universal and in agreement with known and conjectured exact values.

Vladimir S. Dotsenko, Jesper Lykke Jacobsen, Xuan Son Nguyen +1 more

Antonio Coniglio A

N.S. Ananikian, Ruben G. Ghulghazaryan, N. Sh. Izmailian +1 more

The exact solution of a general Z(4) gauge Potts model with a single and double plaquette representation of the action is found on a subspace of gauge-coupling parameters on the square and triangular lattices. The two Ising-type critical lines of a second-order phase transition for the model on a square lattice are found. For the model on a triangular lattice the two critical surfaces of an Ising-type and two nontrivial lines of a second-order phase transition with different critical behavior than on the critical surfaces are found. It is shown that a two-dimensional (2D) general Z(4) gauge Potts model with single and double plaquette representation of the action and a 2D spin-3 / 2 Ising model belong to the same universality class.

Hiromi Otsuka, Masafumi Fujimoto

Abstract We focus on asymptotic correlation functions of off-critical models and propose a universal form possessing the C 4v symmetry and that possessing the C 6v symmetry. The former (the latter) is adaptable to classical spin systems on a square (triangular) lattice. Intriguingly, the C 4v form includes three free parameters—an amplitude A , the modulus k , and a deformation parameter b . Meanwhile, the C 6v form does the two of them, i.e., A and k . To proffer numerical evidence to our proposal, we perform large-scale Monte Carlo (MC) simulations of the Q -state Potts models on square and triangular lattices in the paramagnetic phase. We determine the free parameters to fit the forms to the MC data of correlation functions. Then, we find that both universal forms can describe asymptotic behaviors of correlation functions with high accuracy. Also, the C 4v and C 6v forms yield the equilibrium crystal shapes of the square-lattice and honeycomb-lattice models, respectively. These extracted curves of crystal shapes differ, representing the difference of lattice symmetries. Meanwhile, they are both algebraic curves of genus 1 and can become birationally equivalent if the values of k coincide. Our observation indicates that k provides a new measure for comparing the properties of different models on different lattices in two dimensions.

Jesper Lykke Jacobsen, Hubert Saleur