Related papers: Complexity in Mean-Field Spin-Glass Models: Ising …
We study the large $N$-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed $p$-spin models. Specifically, we show that its empirical spectral measure converges in probability to a…
In these notes the main theoretical concepts and techniques in the field of mean-field spin-glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is…
Approximate inference is central to Bayesian learning, with variational inference (VI) providing a scalable framework for posterior approximation. While mean-field VI often fails in high dimensions, the more refined Bethe approximation,…
We study the residual entropy of a two-dimensional Ising model with crossing and four-spin interactions, both for the case that in zero magnetic field and that in an imaginary magnetic field i({\pi}/2)kT. The spin configurations of this…
We discuss a scheme to implement the relaxion solution to the hierarchy problem with multiple axions, and present a UV-completed model realizing the scheme. All of the $N$ axions in our model are periodic with a similar decay constant $f$…
We solve the spin-1 quantum Ising model with single-ion anisotropy by mapping it onto a series of segmented spin-1/2 transverse Ising chains, separated by the $S^z =0$ states called holes. A recursion formula is derived for the partition…
We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model we test the asymptotic static limit of the Sompolinsky solution showing that it fails to yield a…
Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…
Mean-field spin glasses are families of random energy functions (Hamiltonians) on high-dimensional product spaces. In this paper we consider the case of Ising mixed $p$-spin models, namely Hamiltonians $H_N:\Sigma_N\to {\mathbb R}$ on the…
The paper considers the generalized Ising model in the $2\times2\times\infty$ strip with a Hamiltonian invariant with respect to the central axis of rotation through the angle $\pi/2$, which includes all possible multiplicative interactions…
A spin model which exhibits glassy dynamics has been proposed by Newman and Moore. This model possesses no randomness for exchange interactions. We propose partial trace methods for obtaining static exact solutions of this model under free…
We study the nature of the broken ergodicity in the low temperature phase of Ising spin glass systems, using as a diagnostic tool the spectrum of eigenvalues of the spin-spin correlation function. We show that multiple extensive eigenvalues…
We show that temperature and magnetic field properties of the entanglement between spins on the two-dimensional Shastry-Sutherland lattice can be qualitatively described by analytical results for a qubit tetramer. Exact diagonalization of…
In this paper we study the Parisi variational problem for mixed $p$-spin glasses with Ising spins. Our starting point is a characterization of Parisi measures whose origin lies in the first order optimality conditions for the Parisi…
Replica field theory is used to study the n-dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian,…
We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random $N (\gg 1)$-dimensional Gaussian landscape and confined by a…
In order to study certain questions concerning the distribution of the overlap in Sherrington--Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with…
We present an algorithm for the optimization and thermal equilibration of spin glasses - or more generally, cost functions of the Ising form $H=\sum_{\langle i j\rangle} J_{ij} s_i s_j + \sum_i h_i s_i$, defined on graphs with arbitrary…
We consider the totally asymmetric simple exclusion process (TASEP) on a periodic one-dimensional lattice of L sites. Using Bethe ansatz, we derive parametric formulas for the eigenvalues of its generator in the thermodynamic limit. This…
We study numerically the Sherrington--Kirkpatrick model as function of the magnetic field h, with fixed temperature T=0.6 Tc. We investigate the finite size scaling behavior of several quantities, such as the spin glass susceptibility,…