Related papers: Multicritical point of spin glasses
A spin-glass system with a smooth or fractal outer surface is studied by renormalization-group theory, in bulk spatial dimension d=3. Independently varying the surface and bulk random-interaction strengths, phase diagrams are calculated.…
The thermodynamics of the infinite-range Ising spin glass with p-spin interactions in the presence of an external magnetic field h is investigated analytically using the replica method. We give emphasis to the analysis of the transition…
We show strong evidence for the absence of a finite-temperature spin glass transition for the random-bond Ising model on self-dual lattices. The analysis is performed by an application of duality relations, which enables us to derive a…
A recently proposed curvature renormalization group scheme for topological phase transitions defines a generic `curvature function' as a function of the parameters of the theory and shows that topological phase transitions are signalled by…
We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…
We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the…
Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, the Ising model on multiplex networks with two layers is considered,…
We generalize the de Almeida-Thouless line for the many-body Ising spin glass to the microcanonical ensemble and show that it coincides with the canonical one. This enables us to draw a complete microcanonical phase diagram of this model.
It is proposed to understand finite dimensional spin glasses using a $1/m$ expansion, where $m$ is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
We study the replica free energy surface for a spin glass model near the glassy temperature. In this model the simplicity of the equilibrium solution hides non trivial metastable saddle points. By means of the stability analysis performed…
In these two lectures I review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
We consider the three-dimensional $\pm J$ model defined on a simple cubic lattice and study its behavior close to the multicritical Nishimori point where the paramagnetic-ferromagnetic, the paramagnetic-glassy, and the ferromagnetic-glassy…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
The critical behavior of many physical systems involves two competing $n^{}_1-$ and $n^{}_2-$component order-parameters, ${\bf S}^{}_1$ and ${\bf S}^{}_2$, respectively, with $n=n^{}_1+n^{}_2$. Varying an external control parameter $g$,…
The permutation model is a classical spin system where elements of the symmetric group interact with one another. The partition function of this model is directly related to the entanglement structure of random quantum circuits and random…
Renormalization-group theory predicts that the XXZ antiferromagnet in a magnetic field along the easy Z-axis has asymptotically either a tetracritical phase-diagram or a triple point in the field-temperature plane. Neither experiments nor…
Using computer simulations of an atomistic glass-forming liquid, we investigate the fluctuations of the overlap between a fluid configuration and a quenched reference system. We find that large fluctuations of the overlap develop as…
Within the replica approach to mean-field spin-glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric saddle-point. For general spin-glass…
In recent years scale invariant scattering theory provided the first exact access to the magnetic critical properties of two-dimensional statistical systems with quenched disorder. We show how the theory extends to the overlap variables…