相关论文: No replica symmetry breaking phase in random field…

In this paper, an extension of the random field Ginzburg-Landau model on the hypercubic lattice is considered by adding $p$-spin ($p\geqslant 2$) interactions coupled to general disorders. This new model is called the random field…

It is proved that replica symmetry is not broken in the transverse and longitudinal random field Ising model. In this model, the variance of spin overlap of any component vanishes in any dimension almost everywhere in the coupling constant…

We prove that the variance of spin overlap vanishes in disordered Ising models satisfying the Fortuin-Kasteleyn-Ginibre (FKG) inequality under a uniform field, such as generally distributed random field Ising model, site- and bond-diluted…

We study quantum spin systems with quenched Gaussian disorder. We prove that the variance of all physical quantities in a certain class vanishes in the infinite volume limit. We study also replica symmetry breaking phenomena, where the…

It is shown that the variance of a perturbation Hamiltonian density vanishes in the infinite-volume limit of the perturbed spin systems with quenched disorder. This is proven in a simpler way and under less assumptions than before. A…

It is shown that replica symmetry is not broken in the random field Ising model in any dimension, at any temperature and field strength, except possibly at a measure-zero set of exceptional temperatures and field strengths.

It is proven that the ground state is unique in the Edwards-Anderson model for almost all continuous random exchange interactions, and any excited state with the overlap less than its maximal value has large energy in dimensions higher than…

This work is concerned with the theory of the Random Field Ising Model on the hypercubic lattice, in the presence of a independent disorder with finite fifth moment. We showed the absence of replica symmetry in any dimensions, at any…

A fermionic random matrix model, which is a 0-dimensional version of the SYK model with replicas, is considered. The replica-off-diagonal correlation functions vanish at finite N, but we show that they do not vanish in the large N limit due…

During the last years, through the combined effort of the insight, coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features of the mean field Sherrington-Kirkpatrick…

We give the explicit expression of the infinite volume limit for the random overlap structures appearing in the mean field spin glass model. These structures have the expected factorization property for the cavity fields, and enjoy…

Krzakala, Ricci-Tersenghi and Zdeborova have shown recently that the random field Ising model with non-negative interactions and arbitrary external magnetic field on an arbitrary lattice does not have a static spin glass phase. In this…

The spontaneous symmetry breaking of a continuous symmetry in complex field theory at the exceptional point of the parameter space is known to exhibit interesting phenomena, such as the breakdown of a Higgs mechanism. In this work, we…

We determine the low-energy spectrum and Parisi replica symmetry breaking function for the spin glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal ($h$) fields. We show…

The Ginzburg-Landau model below its critical temperature in a temporally oscillating external field is studied both theoretically and numerically. As the frequency or the amplitude of the external force is changed, a nonequilibrium phase…

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…

Some important rigorous results on phase transitions accompanied by the spontaneous breaking of symmetries in statistical mechanics and relativistic quantum field theory are reviewed. Basic ideas, mainly inspired by quantum field theory,…

We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap $R^{1,2}$…

After projection to the lowest Landau level translational invariance and particle conservation combine into dipole symmetry. We show that the new symmetry forbids spontaneous $U(1)$ symmetry breaking at zero temperature. In the case of the…

We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous…