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We exhibit an uncountable family of extremal inhomogeneous Gibbs measures of the low temperature Ising model on regular tilings of the hyperbolic plane. These states arise as low temperature perturbations of local ground states having a…

Probability · Mathematics 2025-07-25 Matteo D'Achille , Loren Coquille , Arnaud Le Ny

We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent $\tau>2$), for which the random graph has a…

Probability · Mathematics 2011-07-01 Sander Dommers , Cristian Giardinà , Remco van der Hofstad

We analyze the ferromagnetic Ising model on a scale-free tree; the growing random network model with the linear attachment kernel $A_k=k+\alpha$ introduced by [Krapivsky et al.: Phys. Rev. Lett. {\bf 85} (2000) 4629-4632]. We derive an…

Statistical Mechanics · Physics 2015-05-13 Takehisa Hasegawa , Koji Nemoto

We analyze the magnetization and the overlap distributions on the ferromagnetic Cayley tree. Two quantities are investigated: the asymptotic scaling of all the moments of the magnetization and overlap distributions, as well as the…

Condensed Matter · Physics 2009-10-28 R. Mélin

In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the…

Mathematical Physics · Physics 2016-11-25 Aernout van Enter , Victor Ermolaev , Giulio Iacobelli , Christof Kuelske

Ground states of the three dimensional Edwards-Anderson spin glass are computed in the presence of an external magnetic field. Our algorithm is sufficiently powerful for us to treat systems with up to 600 spins. We perform a statistical…

Disordered Systems and Neural Networks · Physics 2009-10-31 J. Houdayer , O. C. Martin

Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For…

Disordered Systems and Neural Networks · Physics 2009-10-31 Alexander K. Hartmann

We consider a nearest-neighbor solid-on-solid (SOS) model, with several spin values $0,1,\ldots,m,$ $m\geq2,$ and nonzero external field, on a Cayley tree of degree $k$ (with $k+1$ neighbors). We are aiming to extend the results of…

Mathematical Physics · Physics 2021-10-14 M. M. Rahmatullaev , O. Sh. Karshiboev

The quantum critical behavior of the Ising glass in a magnetic field is investigated. We focus on the spin glass to paramagnet transition of the transverse degrees of freedom in the presence of finite longitudinal field. We use two…

Strongly Correlated Electrons · Physics 2009-11-10 L. Arrachea , D. Dalidovich , V. Dobrosavljević , M. J. Rozenberg

A new protocol of the zero-field-cooled (ZFC) magnetization process is studied experimentally on an Ising spin-glass (SG) Fe$_{0.50}$Mn$_{0.50}$TiO$_3$ and numerically on the Edwards-Anderson Ising SG model. Although the time scales differ…

Disordered Systems and Neural Networks · Physics 2009-10-31 Lorenzo W. Bernardi , Hajime Yoshino , Koji Hukushima , Hajime Takayama , Aya Tobo , Atsuko Ito

We investigate magnetic properties of a two-dimensional periodic structure with Ising spins and antiferromagnetic nearest neighbor interaction. The structure is topologically equivalent to the Archimedean (3,12^2) lattice. The ground state…

Statistical Mechanics · Physics 2007-05-23 M. J. Krawczyk , K. Malarz , B. Kawecka-Magiera , A. Z. Maksymowicz , K. Kulakowski

We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the…

We study zero--temperature properties of the 3d Edwards--Anderson Ising spin glass on finite lattices up to size $12^3$. Using multicanonical sampling we generate large numbers of groundstate configurations in thermal equilibrium. Finite…

Condensed Matter · Physics 2009-10-22 Bernd A. Berg , Ulrich H. E. Hansmann , Tarik Celik

As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and…

Disordered Systems and Neural Networks · Physics 2008-02-28 Creighton K. Thomas , A. Alan Middleton

We consider the Ising model with competing interactions and a nonzero external field on the Cayley tree of order two. We describe ground states and verify the Peierls condition for the model. Using a contour argument we show the existence…

Mathematical Physics · Physics 2023-07-26 M. M. Rahmatullaev , M. A. Rasulova , J. N Asqarov

We consider the ferromagnetic Ising model on a sequence of graphs $G_n$ converging locally weakly to a rooted random tree. Generalizing [Montanari, Mossel, Sly '11], under an appropriate "continuity" property, we show that the Ising…

Probability · Mathematics 2015-10-30 Anirban Basak , Amir Dembo

The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are…

Disordered Systems and Neural Networks · Physics 2009-10-30 E. Nogueira , S. Coutinho , F. D. Nobre , E. M. F. Curado , J. R. L. de Almeida

A detailed analysis of Monte Carlo data on the two-dimensional Ising spin glass with bimodal interactions shows that the free energy of the model has a nontrivial scaling. In particular, we show by studying the correlation length that much…

Disordered Systems and Neural Networks · Physics 2009-09-29 Helmut G. Katzgraber , L. W. Lee , I. A. Campbell

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a…

Disordered Systems and Neural Networks · Physics 2009-10-31 C. M. Newman , D. L. Stein

We study the fixed-magnetization ferromagnetic Ising model on random $d$-regular graphs for $d\ge 3$ and inverse temperature below the tree reconstruction threshold. Our main result is that for each magnetization $\eta$, the free energy…

Probability · Mathematics 2025-11-21 Reza Gheissari , Will Perkins , Corrine Yap