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The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…
We study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut, and price…
Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely…
A scaling theory of replica symmetry breaking (RSB) in the SK-model is presented in the framework of critical phenomena for the scaling regime of small inverse RSB-orders, small temperatures, small magnetic fields, and near opposite…
In a statistical physics context, inverse problems consist in determining microscopic interactions such that a system reaches a predefined collective state. A complex collective state may be prescribed by specifying the overlap distribution…
Ordering of the Heisenberg spin glass in four dimensions (4D) with the nearest-neighbor Gaussian coupling is investigated by equilibrium Monte Carlo simulations, with particular attention to its spin and chiral orderings. It is found that…
The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…
This paper constitutes the second part of a two-paper series devoted to the systematic study of vector spin glass models whose energy function involves a spin glass part and a general Mattis interaction part. In this paper, we focus on…
We study statistical properties of 3D classical spin glass layer of certain width and infinite length. The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between…
We show that there is no need to modify the Parisi replica symmetry breaking ansatz, by working with $R$ steps of breaking and solving {\it exactly} the discrete stationarity equations generated by the standard ``truncated Hamiltonian" of…
We consider a multi-layer Sherrington-Kirkpatrick spin-glass as a model for deep restricted Boltzmann machines and we solve for its quenched free energy, in the thermodynamic limit and allowing for a first step of replica symmetry breaking.…
We investigate the connection between the well known Sherrington-Kirkpatrick Ising Spin Glass and the corresponding Lattice Gas model by analyzing the relation between their thermodynamical functions. We present results of replica approach…
We discuss a spin glass reminiscent of the Random Energy Model, which allows in particular to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light on the physical meaning of the order…
We use the generic replica symmetric cubic field-theory to study the transition of short range Ising spin glasses in a magnetic field around the upper critical dimension, d=6. A novel fixed-point is found, in addition to the well-known zero…
A short survey is presented on spin--glass--like states characteristics in complex nonmagnetic systems. We discuss the interplay of the interaction structure and symmetry with the classification scenarios of the replica symmetry breaking.…
We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this…
The analysis of the solution with full replica symmetry breaking in the vicinity of $T_c$ of a general spin glass model with reflection symmetry is performed. The leading term in the order parameter function expansion is obtained. Parisi…
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…
We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero field limit the system exactly realizes the…
We prove the convergence in distribution of the fluctuations of the free energy of the mixed $p$-spin Sherrington-Kirkpatrick model with non-vanishing $2$-spin component at high enough temperature. The limit is Gaussian, and the…