Related papers: Replica Symmetry Breaking without Replicas
Simulational studies of spin glasses in the last decade have focussed on the so-called replicon exponent $\alpha$ as a means of determining whether the low-temperature phase of spin glasses is described by the replica symmetry breaking…
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse…
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 existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to the model with a general random exchange interactions. The relation between the expectation value of the…
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 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…
We compute numerically small window overlaps in the three dimensional Edwards Anderson spin glass. We show that they behave in the way implied by the Replica Symmetry Breaking Ansatz, that they do not qualitatively differ from the full…
A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling…
We present a general formalism to make the Replica-Symmetric and Replica-Symmetry-Breaking ansatz in the context of Kikuchi's Cluster Variational Method (CVM). Using replicas and the message-passing formulation of CVM we obtain a…
The whole enterprise of spin compositions can be recast as simple enumerative combinatoric problems. We show here that enumerative combinatorics (EC)\citep{book:Stanley-2011} is a natural setting for spin composition, and easily leads to…
We solve the fermionic version of the Ising spin glass for arbitrary filling \mu and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from \mu to the anisotropy parameter D, we also obtain the…
The full replica symmetry breaking free energy of the Ising spin glass on random regular graphs is given by the solutions of two auxiliary variational problems inside a global (physical) variational problem on the order parameter. In this…
We discuss Gaussian fluctuations in a spin glass model with one replica symmetry breaking. We show how non-perturbative fluctuations of the break-point parameter can be included in the longitudinal propagator within linear response theory.
Recent tensor-network samplings of modified Nishimori spin glasses have revealed robust finite-temperature critical transitions in two dimensions, defying the standard Edwards-Anderson lower critical dimension boundary ($d_{l}\approx2.5$).…
We describe a novel method which allows the treatment of high orders of replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly, without a need for approximations or scaling assumptions. It yields the low temperature…
This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity…
Kernel methods provide a theoretically grounded framework for non-linear and non-parametric learning, with strong analytic foundations and statistical guarantees. Yet, their scalability has long been limited by prohibitive time and memory…
We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on…