Quantum spherical model with competing interactions
| Autor: | Bienzobaz, P. F., Salinas, S. R. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Physica A, 391, 6399, 2012 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.physa.2012.07.027 |
| Popis: | 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 $p=1/4$. Comment: 18 pages, 3 figures, refs added, minor modifications to match published version |
| Databáze: | arXiv |
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