Quantum spherical model with competing interactions

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 $m\le d$ 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 $d\ge 2$, 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 $p=1/4$.

18 pages, 3 figures, refs added, minor modifications to match published version

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• Quantum description of spherical spins
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• Stochastic Quantization of the Spherical Model and Supersymmetry
• Supersymmetric Extension of the Quantum Spherical Model
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• Non-equilibrium dynamics of the open quantum $O(n)$-model with non-Markovian noise: exact results
• Supersymmetric Quantum Spherical Spins with Short-Range Interactions
• Spontaneous Symmetry Breaking and Frustrated Phases
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