Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions

TL;DR

This paper investigates the finite temperature behavior of quantum antiferromagnets in magnetic fields, proposing a universal scaling hypothesis near phase transitions and providing calculations across different dimensions.

Contribution

It introduces the ZERO SCALE-FACTOR UNIVERSALITY hypothesis for $d<2$ and computes scaling properties of experimental observables in various dimensions.

Findings

Scaling properties obey universal behavior near phase transition.

Logarithmic violations occur in two dimensions.

Exact results are obtained for one-dimensional systems.

Abstract

Consider a $d$-dimensional antiferromagnet with a quantum disordered ground state and a gap to bosonic excitations with non-zero spin. In a finite external magnetic field, this antiferromagnet will undergo a phase transition to a ground state with non-zero magnetization, describable as the condensation of a dilute gas of bosons. The finite temperature properties of the Bose gas in the vicinity of this transition are argued to obey a hypothesis of ZERO SCALE-FACTOR UNIVERSALITY for $d < 2$, with logarithmic violations in $d=2$. Scaling properties of various experimental observables are computed in an expansion in $\epsilon=2-d$, and exactly in $d=1$.