# Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

## TL;DR

This study investigates the behavior of generalized susceptibilities in the 3D three-state Potts model, revealing sign changes near phase boundaries and finite-size effects relevant to critical phenomena.

## Contribution

It provides a detailed analysis of the sign distribution and finite-size scaling of susceptibilities in the Potts model across the phase diagram.

## Key findings

- Odd-order susceptibilities change sign between phases.
- Negative fourth-order susceptibility appears near the critical point.
- Finite-size scaling aligns with 3D Ising universality class.

## Abstract

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.