Change in the Order of a Phase Transition in the 2D Potts Model with Equivalent Neighbours

Abstract

Two dimensional Potts model is a classical example where the symmetry of the order parameter controls the order of a phase transition: on a square lattice with nearest-neighbours interaction, when the number of states $q$ is less than or equal to 4, the second-order phase transition is observed, while for $q>4$ the first-order phase transition occurs. Recent research shows that even when the number of states is fixed, increasing the interaction range allows one to reach the point where the order of the phase transition changes. We focus on a $q=3$ 2D Potts model and, from the analysis of the partition function zeros, locate the number of interacting neighbours that change the order of the phase transition.

arXiv comment20 pages, 6 figures

References in corpus (11)

• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Medium-range interactions and crossover to classical critical behavior
• On the role of Fourier modes in finite-size scaling above the upper critical dimension
• Rigorous analysis of discontinuous phase transitions via mean-field bounds
• Critical and tricritical singularities from small-scale Monte Carlo simulations: The Blume-Capel model in two dimensions
• Density of Partition Function Zeroes and Phase Transition Strength
• First-Order Phase Transition in Potts Models with finite-range interactions
• Equivalent-neighbor Potts models in two dimensions
• Critical and tricritical behavior of the $d=3$ Blume-Capel model: Results from small-scale Monte Carlo simulations
• Extracting partition function zeros from Fukui-Todo simulations
• When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension