Thermodynamic characteristics of the classical n-vector magnetic model in three dimensions

TL;DR

This paper develops a microscopic, parameter-free method to calculate thermodynamic properties of the 3D n-vector magnetic model, providing explicit expressions near phase transitions for various n values.

Contribution

It introduces a rigorous analytical approach using collective variables to analyze thermodynamics of the 3D n-vector model without adjustable parameters.

Findings

Explicit formulas for entropy, internal energy, specific heat near critical point

Dependence of thermodynamic amplitudes on microscopic parameters for different n

Foundation for detailed analysis of critical behavior in 3D magnetic systems

Abstract

The method of calculating the free energy and thermodynamic characteristics of the classical n-vector three-dimensional (3D) magnetic model at the microscopic level without any adjustable parameters is proposed. Mathematical description is perfomed using the collective variables (CV) method in the framework of the $\rho^4$ model approximation. The exponentially decreasing function of the distance between the particles situated at the N sites of a simple cubic lattice is used as the interaction potential. Explicit and rigorous analytical expressions for entropy,internal energy, specific heat near the phase transition point as functions of the temperature are obtained. The dependence of the amplitudes of the thermodynamic characteristics of the system for $T>T_c$ and $T<T_c$ on the microscopic parameters of the interaction potential are studied for the cases $n=1,2,3$ and $n\to\infty$. The obtained results provide the basis for accurate analysis of the critical behaviour in three dimensions including the nonuniversal characteristics of the system.