A quantum spherical model of spin glass

Gaetano Busiello, E. V. Gazeeva, I. R. Khaibutdinova +1 more

Alba Theumann, Vilarbo da Silva

Theo M. Nieuwenhuizen

Prabodh Shukla, Sujeeth Kumar Devendar Singh

A phenomenological Langevin-like equation for spin glass dynamics is proposed and solved. The equation reproduces the static spherical model results for spin glass in the long time limit. The magnetisation, order parameter and on-site correlations are found to decay exponentially above the transition temperature and algebraically at and below it, as t to infinity . A closed-form expression for the dynamic susceptibility valid at all temperatures is also obtained.

T. K. Kopeć, Klaus D. Usadel

We consider the short-range-interaction disordered quantum spherical model with a symmetrical binary -bond distribution on the Bethe lattice (with coordination number z ). The system exhibits a quantum phase transition separating the spin-glass and disordered phases, where the quantum effects are regulated by a parameter describing the kinetic energy. The model admits, in the spherical limit, an exact solution both in the spin-glass phase and in the disordered phase. The quantum dynamics is examined via various correlation functions on the infinite tree, which are evaluated in closed form. A closed-form solution for the averaged free energy has been obtained, and various thermodynamic functions are explicitly derived in the form of low-temperature expansions.

Pedro Castro Menezes, Alba Theumann

We show that the effective action of the quantum spherical spin glass is invariant under a generalized form of Becchi-Rouet-Stora-Tyutin supersymmetry. The Ward identities associated with this invariance indicate that the spin glass order parameter must vanish, and as a result the annealed average is exact in this model. We present results for the free energy, entropy, and specific heat. Due to quantum effects, the entropy remains finite and the specific heat vanishes at zero temperature. Results for the phase diagram coincide with those obtained by different formalisms. At zero temperature we derive the scaling behavior with frequency of the dynamical susceptibility.