Quantum spherical model with competing interactions

P.F. Bienzobaz and S.R. Salinas

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 24, 6399-6408

Abstract: We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T, a quantum parameter g, and the ratio p=−J2/J1, where J1>0 refers to ferromagnetic interactions between first-neighbour sites along the d directions of a hypercubic lattice, and J2<0 is associated with competing antiferromagnetic interactions between second neighbours along m≤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, gc=gc(p) for d≥2, with a singularity at the Lifshitz point if d<(m+4)/2. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4.

Keywords: Spherical model; Competing interactions; Lifshitz point; Quantum spherical model; Quantum phase transitions (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:24:p:6399-6408

DOI: 10.1016/j.physa.2012.07.027

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