First and second order transitions in dilute O(n) models

TL;DR

This paper investigates the phase transitions of a dilute O(n) model on a honeycomb lattice, revealing a transition from critical to first-order behavior and identifying a tricritical point connecting different universality classes.

Contribution

It introduces a comprehensive analysis of the phase diagram of the dilute O(n) model using finite-size scaling and transfer-matrix methods, including the loop representation for non-integer n.

Findings

Critical points of known universality class at low vacancy activity

First-order transition at high vacancy activity

Identification of a tricritical point interpolating between theta and Ising universality classes

Abstract

We explore the phase diagram of an O(n) model on the honeycomb lattice with vacancies, using finite-size scaling and transfer-matrix methods. We make use of the loop representation of the O(n) model, so that $n$ is not restricted to positive integers. For low activities of the vacancies, we observe critical points of the known universality class. At high activities the transition becomes first order. For n=0 the model includes an exactly known theta point, used to describe a collapsing polymer in two dimensions. When we vary $n$ from 0 to 1, we observe a tricritical point which interpolates between the universality classes of the theta point and the Ising tricritical point.