q-state Potts model on the Apollonian network

TL;DR

This study investigates the q-state Potts model on the Apollonian network using Monte Carlo and Transfer Matrix methods, revealing no critical behavior and proposing new scaling functions.

Contribution

It introduces a combined Monte Carlo and Transfer Matrix approach to analyze the Potts model on complex networks, with new scaling functions and no observed criticality.

Findings

No critical behavior in the thermodynamic limit for any q

Quantitative agreement between Monte Carlo and Transfer Matrix results

Proposed new scaling functions in temperature and q

Abstract

The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the Transfer Matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of temperature for different number of states, $q$. Different scaling functions in temperature and $q$ are proposed. A quantitative agreement is found between results from both methods. No critical behavior is observed in the thermodynamic limit for any number of states.