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The growing correlation length observed in supercooled liquids as their temperature is lowered has been studied with the aid of a single occupancy cell model. This model becomes more accurate as the density of the system is increased. One…

Statistical Mechanics · Physics 2013-04-17 Christopher J. Fullerton , M. A. Moore

We prove universality of spin correlations in the scaling limit of the planar Ising model on isoradial graphs with uniformly bounded angles and Z-invariant weights. Specifically, we show that in the massive scaling limit, i.e., as the mesh…

Probability · Mathematics 2021-04-28 Dmitry Chelkak , Konstantin Izyurov , Rémy Mahfouf

Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is…

High Energy Physics - Theory · Physics 2008-11-26 A. I. Bugrij , O. Lisovyy

We consider continuous time random interlacements on $\mathbb{Z}^d$, $d \ge 3$, and characterize the distribution of the corresponding stationary random field of occupation times. When d = 3, we relate this random field to the…

Probability · Mathematics 2012-10-30 Alain-Sol Sznitman

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size…

Statistical Mechanics · Physics 2015-02-18 E. J. Flores-Sola , B. Berche , R. Kenna , M. Weigel

We present numerical simulations of the random field Ising model in three dimensions at zero temperature. The critical exponents are found to agree with previous results. We study the magnetic susceptibility by applying a small magnetic…

Disordered Systems and Neural Networks · Physics 2014-03-21 Marco Picco , Nicolas Sourlas

We present analytical results for the strongly anisotropic random field Ising model, consisting of weakly interacting spin chains. We combine the mean-field treatment of interchain interactions with an analytical calculation of the average…

Statistical Mechanics · Physics 2009-10-31 Marc Thilo Figge , Maxim V. Mostovoy , Jasper Knoester

We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…

High Energy Physics - Theory · Physics 2022-07-04 Minjae Cho , Barak Gabai , Ying-Hsuan Lin , Victor A. Rodriguez , Joshua Sandor , Xi Yin

An extension of the Ising spin configurations to continuous functions is used for an exact representation of the Random Field Ising Model's order parameter in terms of disagreement percolation. This facilitates an extension of the recent…

Mathematical Physics · Physics 2022-01-25 Michael Aizenman , Matan Harel , Ron Peled

We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from minus…

Statistical Mechanics · Physics 2009-10-28 Deepak Dhar , Prabodh Shukla , James P. Sethna

Transfer-matrix methods are used to study the probability distributions of spin-spin correlation functions $G$ in the two-dimensional random-field Ising model, on long strips of width $L = 3 - 15$ sites, for binary field distributions at…

Statistical Mechanics · Physics 2009-10-31 S. L. A. de Queiroz , R. B. Stinchcombe

Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, generally we expect both…

Statistical Mechanics · Physics 2011-08-12 Taro Nakada , Per Arne Rikvold , Takashi Mori , Masamichi Nishino , Seiji Miyashita

The spatial distribution of persistent spins at zero-temperature in the pure two-dimensional Ising model is investigated numerically. A persistence correlation length, $\xi (t)\sim t^Z$ is identified such that for length scales $r<<\xi (t)$…

Statistical Mechanics · Physics 2009-10-31 S. Jain , H. Flynn

The bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field…

High Energy Physics - Theory · Physics 2008-11-26 Sean M. Carroll , Miguel E. Ortiz , Washington Taylor

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($T_{o}$). Detailed balance is violated so that the spin…

Statistical Mechanics · Physics 2009-11-07 B. Schmittmann , F. Schmueser

The energy-energy correlation function of the two-dimensional Ising model with weakly fluctuating random bonds is evaluated in the large scale limit. Two correlation lengths exist in contrast to one correlation length in the pure 2D Ising…

Condensed Matter · Physics 2007-05-23 K. Ziegler

Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical…

Statistical Mechanics · Physics 2014-10-15 Louis Colonna-Romano , Harvey Gould , W. Klein

We consider the Ising model at its critical temperature with external magnetic field $ha^{15/8}$ on the square lattice with lattice spacing $a$. We show that the truncated two-point function in this model decays exponentially with a rate…

Probability · Mathematics 2019-09-09 Federico Camia , Jianping Jiang , Charles M. Newman

Transfer-matrix methods are used, in conjunction with finite-size scaling and conformal invariance concepts, to generate an accurate phase diagram for a two-dimensional square-lattice Ising spin-1/2 magnet, with couplings which are positive…

Statistical Mechanics · Physics 2009-10-23 S. L. A. de Queiroz

We enlighten some critical aspects of the three-dimensional ($d=3$) random-field Ising model from simulations performed at zero temperature. We consider two different, in terms of the field distribution, versions of model, namely a Gaussian…

Disordered Systems and Neural Networks · Physics 2015-01-13 P. E. Theodorakis , N. G. Fytas