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Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.


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TL;DR: In this paper, Monte Carlo simulations are presented for a model of a symmetrical polymer mixture on the simple cubic lattice, modeling both polymers A, B by self-avoiding walks of NA=NB=N steps.
Abstract: Monte Carlo simulations are presented for a model of a symmetrical polymer mixture on the simple cubic lattice, modeling both polymers A, B by self‐avoiding walks of NA=NB=N steps. If a pair of nearest‐neighbor sites is taken by monomers of the same species, an energy e is won. In the Monte Carlo algorithm local motions of the chains are considered (allowing for 20% vacancies to ensure enough chain mobility) as well as transformations of A chains into B chains and vice versa, since the simulation applies the grand‐canonical ensemble where the chemical potential difference rather than the volume fraction is fixed. The phase diagram, the excess specific heat, and the structure factor in the long‐wavelength limit are obtained for N=4, 8, 16, and 32 using finite L×L×L lattices with L ranging from 8 to 20. Analyzing these results with finite size scaling techniques, both critical exponents and critical amplitudes are estimated. Although the exponents are consistent with those of the three‐dimensional Ising mod...

221 citations

Journal ArticleDOI
TL;DR: A classical spin-one lattice gas model is used to study the competition between short-range ferromagnetic coupling and long-range antiferromagnetic Coulomb interactions in high-temperature superconductors.
Abstract: A classical spin-one lattice gas model is used to study the competition between short-range ferromagnetic coupling and long-range antiferromagnetic Coulomb interactions. The model is a coarse-grained representation of frustrated phase separation in high-temperature superconductors. The ground states are determined for the complete range of parameters by using a combination of numerical and analytical techniques. The crossover between ferromagnetic and antiferromagnetic states proceeds via a rich structure of highly symmetric striped and checkerboard phases. There is no devil's staircase behavior because mixtures of stripes with different period phase separate.

221 citations

Journal ArticleDOI
Conyers Herring1, C. Kittel1
TL;DR: The theory of spin waves, leading to the Bloch √ 3 √ 2 √ 1/3 2/2 ) law for the temperature variation of saturation magnetization, is discussed for ferromagnetic insulators and metals in this paper.
Abstract: The theory of spin waves, leading to the Bloch ${T}^{\frac{3}{2}}$ law for the temperature variation of saturation magnetization, is discussed for ferromagnetic insulators and metals, with emphasis on its relation to the theory of the energy of the Bloch interdomain wall The analysis indicates that spin-wave theory is of more general validity than the Heitler-London-Heisenberg model from which it was originally derived Many properties of spin waves of long wavelength can be derived without specialized assumptions, by a field-theoretical treatment of the ferromagnetic material as a continuous medium in which the densities of the three components of spin are regarded as amplitudes of a quantized vector field As applications, the effects of anisotropy energy and magnetic forces are calculated; and it is shown that the Holstein-Primakoff result for the field dependence of the saturation magnetization can be derived in an elementary manner An examination of the conditions for validity of the field theory indicates that it should be valid for insulators, and probably also for metals, independently of any simplifying assumptions The connection with the itinerant electron model of a metal is discussed; it appears that this model is incomplete in that it omits certain spin wave states which can be proved to exist, and that when these are included, it will yield both a magnetization reversal proportional to ${T}^{\frac{3}{2}}$ and a specific heat proportional to $T$ Incidental results include some insight into the relation between the exchange and Ising models for a two-dimensional lattice, an upper limit to the effective exchange integral, and a treatment of spin waves in rhombic lattices

221 citations

Journal ArticleDOI
TL;DR: In this article, the problem of an Ising model with random nearest-neighbor interactions is reformulated to make manifest Toulouse's recent suggestion that a broken "lattice gauge symmetry" is responsible for the unusual properties of spin glasses.
Abstract: The problem of an Ising model with random nearest-neighbor interactions is reformulated to make manifest Toulouse's recent suggestion that a broken "lattice gauge symmetry" is responsible for the unusual properties of spin glasses. Exact upper and lower bounds on the ground-state energy for models in which the interactions are of constant magnitude but fluctuating sign are obtained, and used to place restrictions on possible geometries of the unsatisfied interactions which must be present in the ground state. Proposed analogies between the ferromagnet---spin-glass phase boundary at zero temperature and a percolation threshold for the "strings" of unsatisfied bonds are reviewed in the light of this analysis. Monte Carlo simulations show that the upper bound resulting from a "one-dimensional approximation" to the spin-glass ground-state energy is reasonably close to the actual result. The transition between spin glass and ferromagnet at 0 K appears to be weakly first order in these models. The entropy of the ground state is obtained from the temperature dependence of the internal energy, and compared with the density of free spins at very low temperatures. For a two-dimensional spin glass in which half the bonds are antiferromagnetic, $S(0)\ensuremath{\approx}0.099{k}_{B}$; for the analogous three-dimensional spin glass the result is $S(0)\ensuremath{\approx}0.062{k}_{B}$. Monte Carlo kinetic simulations are reported which demonstrate the existence and stability of a field-cooled moment in the spin-glass ground state.

221 citations

Journal ArticleDOI
TL;DR: The phase diagram in the H_t−T plane is determined via magnetic susceptibility measurements and a solution of the full mean-field Hamiltonian using the known LiHoF_4 crystal-field wave functions, including nuclear hyperfine terms, accurately matches experiment.
Abstract: The classical, thermally driven transition in the dipolar-coupled Ising ferromagnet LiHoF_4 (T_c=1.53K) can be converted into a quantum transition driven by a transverse magnetic field H_t at T=0. The transverse field, applied perpendicular to the Ising axis, introduces channels for quantum relaxation, thereby depressing T_c. We have determined the phase diagram in the H_t−T plane via magnetic susceptibility measurements. The critical exponent, γ=1, has a mean-field value in both the classical and quantum limits. A solution of the full mean-field Hamiltonian using the known LiHoF_4 crystal-field wave functions, including nuclear hyperfine terms, accurately matches experiment.

220 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023682
20221,314
2021854
2020947
2019870
2018844