Field-induced Bose-Einstein condensation of interacting dilute magnons in three-dimensional spin systems: A renormalization-group study

TL;DR

This study uses renormalization-group methods to analyze how magnetic fields influence Bose-Einstein condensation of dilute magnons in three-dimensional spin systems, revealing different temperature dependencies based on symmetry class and anisotropy.

Contribution

It provides a detailed theoretical analysis of the magnetic field dependence on critical temperature in 3D spin systems with different symmetries and anisotropies, using renormalization-group techniques.

Findings

Power law $[H_c(T)-H_c(0)] o T^2$ for SU(2) symmetry

Linear $[H_c(T)-H_c(0)] o T$ dependence for U(1) symmetry

$T^{3/2}$ dependence when including anisotropy

Abstract

We use the Renormalization Group method to study the magnetic field influence on the Bose-Einstein condensation of interacting dilute magnons in three dimensional spin systems. We first considered a model with SU(2) symmetry (universality class $z=1$) and we obtain for the critical magnetic field a power law dependence on the critical temperature, $[H_c(T)-H_c(0)]\sim T^2$. In the case of U(1) symmetry (universality class $z=2$) the dependence is different, and the magnetic critical field depends linearly on the critical temperature, $[H_c(T)-H_c(0)]\sim T$. By considering a more relevant model, which includes also the system's anisotropy, we obtain for the same symmetry class a $T^{3/2}$ dependence of the magnetic critical field on the critical temperature. We discuss these theoretical predictions of the renormalization group in connection with experimental results reported in the literature.