Phase boundary and finite temperature crossovers of the quantum Ising model in two dimensions

TL;DR

This paper investigates the phase boundary and finite temperature crossovers in the 2D quantum Ising model near its quantum critical point using renormalization group flows, revealing how quantum and thermal fluctuations shape critical behavior.

Contribution

It derives and analyzes RG flow equations to understand the interplay of quantum and thermal fluctuations near the quantum critical point in the 2D quantum Ising model.

Findings

Finite temperature crossovers are characterized by critical exponents.

The phase boundary follows a power law with the zero-temperature correlation length exponent.

The results confirm predictions from epsilon-expansion theory.

Abstract

We revisit the two-dimensional quantum Ising model by computing renormalization group flows close to its quantum critical point. The low but finite temperature regime in the vicinity of the quantum critical point is squashed between two distinct non-Gaussian fixed points: the classical fixed point dominated by thermal fluctuations and the quantum critical fixed point dominated by zero-point quantum fluctuations. Truncating an exact flow equation for the effective action we derive a set of renormalization group equations and analyze how the interplay of quantum and thermal fluctuations, both non-Gaussian in nature, influences the shape of the phase boundary and the region in the phase diagram where critical fluctuations occur. The solution of the flow equations makes this interplay transparent: we detect finite temperature crossovers by computing critical exponents and we confirm that the power law describing the finite temperature phase boundary as a function of control parameter is given by the correlation length exponent at zero temperature as predicted in an epsilon-expansion with epsilon=1 by Sachdev, Phys. Rev. B 55, 142 (1997).