Quantum spherical model with competing interactions

TL;DR

This paper studies the phase diagram of a quantum spherical model with competing ferromagnetic and antiferromagnetic interactions, revealing critical points, phase boundaries, and correlation decay behaviors across different dimensions.

Contribution

It extends classical spherical model results to the quantum case, analyzing the effects of quantum fluctuations and competing interactions on phase transitions and critical phenomena.

Findings

Identifies the topology of the critical line in the quantum model.

Derives the decay of pair correlations in one dimension.

Establishes critical dimensions and analyzes quantum critical behavior near the Lifshitz point.

Abstract

We analyze the phase diagram of a quantum mean spherical model in terms of the temperature $T$, a quantum parameter $g$, and the ratio $p=-J_{2}/J_{1}$, where $J_{1}>0$ refers to ferromagnetic interactions between first-neighbor sites along the $d$ directions of a hypercubic lattice, and $J_{2}<0$ is associated with competing antiferromagnetic interactions between second neighbors along $m\leq d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the $g=0$ space, with a Lifshitz point at $p=1/4$, for $d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0 phase diagram, there is a critical border, $g_{c}=g_{c}(p) $ for $d\geq2$, with a singularity at the Lifshitz point if $d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyze the quantum critical behavior in the neighborhood of $p=1/4$.