Partial long-range order in antiferromagnetic Potts models

TL;DR

This paper investigates partial long-range order in antiferromagnetic Potts models on various 2D lattices using tensor-based numerical methods, revealing complex phase transitions and the influence of lattice irregularity.

Contribution

It provides a comprehensive numerical analysis of partial long-range order in antiferromagnetic Potts models across different lattices and values of q, highlighting new phenomena.

Findings

Identification of entropy-driven phase transitions

Role of lattice irregularity in ordering

Large critical q values and double phase transitions

Abstract

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered. This situation may arise from frustration of the interactions, but also from an irregular but unfrustrated lattice structure. We study partial long-range order in a range of antiferromagnetic $q$-state Potts models on different two-dimensional lattices and for all relevant values of $q$. We exploit the power of tensor-based numerical methods to evaluate the partition function of these models and hence to extract the key thermodynamic properties -- entropy, specific heat, magnetization, and susceptibility -- giving deep insight into the phase transitions and ordered states of each system. Our calculations reveal a range of phenomena related to partial ordering, including different types of entropy-driven phase transition, the role of lattice irregularity, very large values of the critical $q_c$, and double phase transitions.