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Quantum spherical model with competing interactions


  • Bienzobaz, P.F.
  • Salinas, S.R.


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.

Suggested Citation

  • Bienzobaz, P.F. & Salinas, S.R., 2012. "Quantum spherical model with competing interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6399-6408.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6399-6408
    DOI: 10.1016/j.physa.2012.07.027

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