Evolution of phase transition in the finite-fugacity extended dimer model

TL;DR

This study explores how the nature of phase transitions in a classical dimer model on a square lattice changes with varying fugacity, revealing a progression from Kosterlitz-Thouless to first-order transitions.

Contribution

It demonstrates the dependence of phase transition order on fugacity in the extended dimer model using Monte Carlo simulations, uncovering a transition from KT to first-order phases.

Findings

Phase transition order depends on fugacity.

Transition evolves from KT to high-order and then to first-order.

Correlation functions show evolving decay behavior.

Abstract

We investigate the evolution of phase transition of the classical fully compact dimer model on the bipartite square lattice with second nearest bonds at finite temperatures. We use the numeric Monte Carlo method with the directed-loop algorithm to simulate the model. Our results show that the order of the phase transition depends on the fugacity of the second nearest bonds. We find that the phase transition reduces from the Kosterlitz-Thouless transition to unconventional high-order phase transitions which feature the coexistence of properties Kosterliz-Thouless transition and the first-order phases transition simultaneously. As the fugacity increases further, phase transition evolves to the first-order phase transition. In addition, our results of dimer-dimer correlation functions and their corresponding structure factor functions computed by us show the evolution of decay correlation for different fugacity.