Stripe-tetragonal phase transition in the 2D Ising model with dipole interactions: Partition-function zeros approach

TL;DR

This study uses partition function zeros from multicanonical simulations to clarify the nature of phase transitions in the 2D dipolar Ising model, confirming a single second-order transition line and excluding a tricritical point.

Contribution

It provides a definitive analysis of the phase transition order in the 2D dipolar Ising model using partition function zeros, resolving previous controversies.

Findings

Critical exponents consistent with a single second-order transition

Excludes the existence of a tricritical point in the studied region

Supports conclusions with specific heat and susceptibility analysis

Abstract

We have performed multicanonical simulations to study the critical behavior of the two-dimensional Ising model with dipole interactions. This study concerns the thermodynamic phase transitions in the range of the interaction \delta where the phase characterized by striped configurations of width h=1 is observed. Controversial results obtained from local update algorithms have been reported for this region, including the claimed existence of a second-order phase transition line that becomes first order above a tricritical point located somewhere between \delta=0.85 and 1. Our analysis relies on the complex partition function zeros obtained with high statistics from multicanonical simulations. Finite size scaling relations for the leading partition function zeros yield critical exponents \nu that are clearly consistent with a single second-order phase transition line, thus excluding such tricritical point in that region of the phase diagram. This conclusion is further supported by analysis of the specific heat and susceptibility of the orientational order parameter.