A Monte Carlo simulation of Ising chains with competing short-range and infinite-range interactions has been carried out. Results show that whenever the system does not enter a metastable state, variation of temperature brings about phase transitions in the Ising chain. These phase transitions, except for two sets of interaction strengths are generally of higher order and involve changes in the long-range while the short-range order remains unaffected.

Journal of Physics C Solid State PhysicsNov 14, 19780 citations

Some Monte-Carlo Studies of the Ising Model

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Springer proceedings in physicsJan 1, 19941 citation

Annals of the Israel Physical Society

A Monte Carlo study of coupled Ising chains

D. P. Landau, Tom Graim

Published Jan 1, 1978• 0 citations

OpenAlex

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_{12}

_{29}

and also, conceptually, as a geometry which is intermediate between one and two dimensions. Using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we find that the crossover of the magnetization critical exponent from the Ising to tricritical Ising value shows an unusual non-monotonic behavior.

Monte Carlo calculations have been used to study the behavior of a simple cubic spin-\textonehalf{} Ising model with spatially anisotropic nearest-neighbor coupling. The interaction in the

x

and

y

directions, which is equal to (${J}_{\ensuremath{\perp}}$), was systematically decreased compared to that in the

z

direction (${J}_{\ensuremath{\parallel}}$), and results were obtained for values of $\ensuremath{\Delta}=\frac{{J}_{\ensuremath{\perp}}}{{J}_{\ensuremath{\parallel}}}$ as small as 0.003. For small $\ensuremath{\Delta}$ the system behaves like a one-dimensional Ising chain at high temperature before undergoing a low-temperature transition to a three-dimensionally ordered state. We find that the asymptotic ($\ensuremath{\Delta}\ensuremath{\rightarrow}0$) variation of

{T}_{c}

is accurate over a surprisingly wide range of $\ensuremath{\Delta}$.