Boundary and Bulk Phase Transitions in the Two Dimensional Q > 4 State Potts Model

TL;DR

This paper investigates the surface and bulk phase transitions of the two-dimensional Q > 4 state Potts model using exact solutions and numerical methods, revealing universal surface behavior and detailed bulk transition characteristics.

Contribution

It provides the first complete analytical solution for the surface transition in the Q → ∞ limit and demonstrates the universality of surface transition properties for all Q > 4.

Findings

Surface transition universality class is independent of Q > 4

Exact analytical results for Q → ∞ limit including critical exponents

Numerical calculations of latent heat and magnetization discontinuity

Abstract

The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q \to \infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point.