Related papers: Spin glasses on Bethe Lattices for large coordinat…
Spin glass models involving multiple replicas with constrained overlaps have been studied in [FPV92; PT07; Pan18a]. For the spherical versions of these models [Ko19; Ko20] showed that the limiting free energy is given by a Parisi type…
The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the…
We show that the only solutions of the TAP equations for the Sherrington-Kirkpatrick model of Ising spin glasses which can be found by iteration are those whose free energy lies on the border between replica symmetric and broken replica…
We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures $\beta>0$. To characterize the free energy,…
We study the Ising spin glass on random graphs with fixed connectivity z and with a Gaussian distribution of the couplings, with mean \mu and unit variance. We compute exact ground states by using a sophisticated branch-and-cut method for…
The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain…
We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas $n$…
We consider identical copies of spin glasses in finite dimension coupled at the boundaries. This allows to identify the spin glass analogous of twisted boundary conditions in ferromagnetic system and leads to the definition of an interface…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed…
We analyze the spontaneous $U(1)_R$ symmetry breaking at finite temperature for the simple O'Raifeartaigh-type model introduced in [1] in connection with spontaneous supersymmetry breaking. We calculate the finite temperature effective…
We consider $N$ i.i.d. Ising spins with mean $m\in (-1,1)$ whose interactions are described by a Sherrington-Kirkpatrick Hamiltonian with a quartic correction. This model was recently introduced by Bolthausen in \cite{Bolt2} as a toy model…
We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the…
A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field…
Three different vortex glass models are studied by examining the energy barrier against vortex motion across the system. In the two-dimensional gauge glass this energy barrier is found to increase logarithmically with system size which is…
We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We…
The peak of the spin glass relaxation rate, S(t)=d{-M_{TRM}(t,t_w)}/H/{d ln t}, is directly related to the typical value of the free energy barrier which can be explored over experimental time scales. A change in magnetic field H generates…
These notes give an introduction to the physics of the infinite range version of the Edwards--Anderson model, the so-called Sherrington--Kirkpatrick model. In a first part, I motivate and introduce the Edwards--Anderson and…
We compute the probability of positive large deviations of the free energy per spin in mean-field Spin-Glass models. The probability vanishes in the thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the…
We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards-Anderson spin glass model with bimodal couplings (J=+/-1) on a 3D lattice. By using exact reduction…