On the Phase Diagram of the q->1 Extended Potts Model and Lattice Animal Collapse

TL;DR

This paper explores the phase diagram of the extended q-states Potts model as q approaches 1, revealing a line of theta transitions in lattice animals through exact and renormalization methods.

Contribution

It provides an exact solution on the Bethe lattice and a renormalization group analysis, offering new insights into the phase transitions of lattice animals in the q->1 limit.

Findings

Identifies a line of theta transitions from extended to compact phases.

Predicts phase behavior consistent with previous numerical studies.

Uses exact and renormalization group methods for analysis.

Abstract

The phase diagram of the two-dimensional extended q-states Potts model is investigated in the q->1 limit. This is equivalent to studying the phase diagram of a two-dimensional infinite interacting lattice animal. An exact solution on the Bethe lattice and a Migdal-Kadanoff renormalization group calculation predict a line of theta transitions from an extended to a compact phase in the lattice animal. We compare this with the phase diagram predicted from previous numerical studies.