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 versio

In this work, we present a supersymmetric extension of the quantum spherical model, both in components and also in the superspace formalisms. We find the solution for short-and long-range interactions through the imaginary time formalism path integral approach. The existence of critical points (classical and quantum) is analyzed and the corresponding critical dimensions are determined.

We establish the equivalence between the continuum limit of the quantum spherical model with competing interactions, which is relevant to the investigation of Lifshitz points, and the OðNÞ nonlinear sigma model with the addition of higher order spatial derivative operators, which breaks the Lorentz symmetry and is known as Lifshitz-type (or anisotropic) nonlinear sigma model. In the context of the 1=N expansion, we also discuss the renormalization properties of this nonlinear sigma model and find the nontrivial fixed points of the functions in various dimensions, which turn out to be connected with the existence of phase transitions in the quantum spherical model.

In this work we investigate properties of a supersymmetric extension of the quantum spherical model from an off-shell formulation directly in the superspace. This is convenient to safely handle the constraint structure of the model in a way compatible with supersymmetry. The model is parametrized by an interaction energy, U r,r ′ , which governs the interactions between the superfields of different sites. We briefly discuss some consequences when U r,r ′ corresponds to the case of first-neighbor interactions. After computing the partition function via saddle point method for a generic interaction, U r,r ′ ≡ U (|r − r ′ |), we focus in the mean-field version, which reveals an interesting critical behavior. In fact, the mean-field supersymmetric model exhibits a quantum phase transition without breaking supersymmetry at zero temperature, as well as a phase transition at finite temperature with broken supersymmetry. We compute critical exponents of the usual magnetization and susceptibility in both cases of zero and finite temperature. Concerning the susceptibility, there are two regimes in the case of finite temperature characterized by distinct critical exponents. The entropy is well behaved at low temperature, vanishing as T → 0. * Electronic address: lgsantos@uel.br † Electronic address: ltavares@uel.br ‡ Electronic address: paulabienzobaz@uel.br § Electronic address: pedrogomes@uel.br F r in order to obtain an off-shell supersymmetry). The supersymmetric model is exactly soluble

As propriedades termodinâmicas do modelo esférico médio do ferromagnetismo, na versão de Curie-Weiss, que inclui interações entre todos os pares de variáveis de spin, podem ser obtidas de maneira exata e analisadas de forma particularmente simples e pedagógica. Torna-se então interessante considerar uma versão quântica desse modelo, que vamos denominar "modelo esférico quântico elementar ", e que também pode ser analisada detalhadamente, em termos da temperatura T e de um parâmetro g associado às flutuações quânticas. Esse sistema proporciona um dos exemplos mais simples de uma transição de fase quântica. Mantendo o estilo pedagógico, fazemos contato com diversos resultados da literatura e apresentamos comentários sobre certas questões, como a correção de anomalias do comportamento clássico e o papel do limite termodinâmico no estabelecimento de uma singularidade do "tipo Bose-Einstein".