Gas of self-avoiding loops on the brickwork lattice

TL;DR

This paper provides an exact analysis of a loop gas model with bending energy on the brickwork lattice, revealing complex phase transitions including a Lifshitz tricritical point and Ising-class transitions at lower densities.

Contribution

It presents the first exact phase diagram for a self-avoiding loop gas with bending energy on the brickwork lattice, including critical exponents and transition lines.

Findings

Identifies a Lifshitz tricritical point in the dense limit.

Discovers Ising universality class transitions at lower densities.

Finds disorder lines associated with tricritical points.

Abstract

An exact calculation of the phase diagram for a loop gas model on the brickwork lattice is presented. The model includes a bending energy. In the dense limit, where all the lattice sites are occupied, a phase transition occuring at an asymmetric Lifshitz tricritical point is observed as the temperature associated with the bending energy is varied. Various critical exponents are calculated. At lower densities, two lines of transitions (in the Ising universality class) are observed, terminated by a tricritical point, where there is a change in the modulation of the correlation function. To each tricritical point an associated disorder line is found.