(Received ) This paper investigates the generalized McCoy-Wu type random Ising model. It is found that boundary magnetization behaves as (TciT) fl 0 , fl 0 = 1:0 just below the ’critical temperature’. From numerical analyses it is revealed that this type of critical behavior, fl 0 = 1:0, would be universal for any type of randomness. This universal behavior is explained in terms of the destruction of the devil’s staircase structure. As an observable result of this model, the integrated distribution function of boundary magnetization is suggested.(Received ) This paper investigates the generalized McCoy-Wu type random Ising model. It is found that boundary magnetization behaves as (TciT) fl 0 , fl 0 = 1:0 just below the ’critical temperature’. From numerical analyses it is revealed that this type of critical behavior, fl 0 = 1:0, would be universal for any type of randomness. This universal behavior is explained in terms of the destruction of the devil’s staircase structure. As an observable result of this model, the integrated distribution function of boundary magnetization is suggested.

Mar 20, 19880 citations

Two-dimensional Ising model in an annealed random field: Exact results

L.L. Gonçalves, Robin B. Stinchcombe

The effect of a discrete distribution of annealed random fields on the properties of the two-dimensional Ising model is studied. The random field is allowed to assume the values 0,\ifmmode\pm\else\textpm\fi{}h with the probabilities ${p}_{0}$ ,${p}_{\ifmmode\pm\else\textpm\fi{}}$, and a parameter \ensuremath{\mu} is introduced which is determined by specifying ${p}_{0}$ . Exact results are obtained by mapping the model onto an effective Ising model on the rectangular lattice without field, and the probabilities ${p}_{0}$ ,${p}_{\ifmmode\pm\else\textpm\fi{}}$ are expressed in terms of the magnetization and two-spin correlations of the effective model. It is shown that the long-range order is not destroyed by the random field and the transition temperature increases as ${p}_{0}$ decreases. For a given ${p}_{0}$ the critical temperature increases with the field strength and these combined effects show that the annealed random field favors the ordering of the system, therefore presenting behavior opposite to that expected for the system in a quenched random field.The effect of a discrete distribution of annealed random fields on the properties of the two-dimensional Ising model is studied. The random field is allowed to assume the values 0,\ifmmode\pm\else\textpm\fi{}h with the probabilities ${p}_{0}$,${p}_{\ifmmode\pm\else\textpm\fi{}}$, and a parameter \ensuremath{\mu} is introduced which is determined by specifying ${p}_{0}$. Exact results are obtained by mapping the model onto an effective Ising model on the rectangular lattice without field, and the probabilities ${p}_{0}$,${p}_{\ifmmode\pm\else\textpm\fi{}}$ are expressed in terms of the magnetization and two-spin correlations of the effective model. It is shown that the long-range order is not destroyed by the random field and the transition temperature increases as ${p}_{0}$ decreases. For a given ${p}_{0}$ the critical temperature increases with the field strength and these combined effects show that the annealed random field favors the ordering of the system, therefore presenting behavior opposite to that expected for the system in a quenched random field.

Physical review. B, Condensed matterApr 1, 19863 citations

Magnetization at corners in two-dimensional Ising models

Michael N. Barber, Ingo Peschel, Paul A. Pearce

Journal of Statistical PhysicsDec 1, 198471 citations

Surface and corner magnetizations in the two-dimensional Ising model

Christian Kaiser, Ingo Peschel

Journal of Statistical PhysicsFeb 1, 198933 citations

The Two-Dimensional Random Bond Ising Model at Criticality—A Monte Carlo Study

Jian‐Sheng Wang, Walter Selke, Vl.S. Dotsenko +1 more

The two-dimensional random bond Ising model with two distinct ferromagnetic nearest-neighbour couplings, J and J ', distributed randomly over the lattice with concentration 1/2 is studied for various ratios J '/ J at criticality. The critical temperature is exactly known from self-duality. The size-dependent specific heat shows a crossover from the perfect Ising to the randomness-dominated critical behaviour of doubly logarithmic form. In the latter region, our estimates for the critical exponents of the size-dependent magnetization and susceptibility are in very good agreement with analytic results suggesting β/ν = 1/8 and γ/ν = 7/4.The two-dimensional random bond Ising model with two distinct ferromagnetic nearest-neighbour couplings, J and J ', distributed randomly over the lattice with concentration 1/2 is studied for various ratios J '/ J at criticality. The critical temperature is exactly known from self-duality. The size-dependent specific heat shows a crossover from the perfect Ising to the randomness-dominated critical behaviour of doubly logarithmic form. In the latter region, our estimates for the critical exponents of the size-dependent magnetization and susceptibility are in very good agreement with analytic results suggesting β/ν = 1/8 and γ/ν = 7/4.

Europhysics Letters (EPL)Feb 15, 199074 citations

{p}_{0}

,${p}_{\ifmmode\pm\else\textpm\fi{}}$, and a parameter \ensuremath{\mu} is introduced which is determined by specifying

{p}_{0}

. Exact results are obtained by mapping the model onto an effective Ising model on the rectangular lattice without field, and the probabilities

{p}_{0}

,${p}_{\ifmmode\pm\else\textpm\fi{}}$ are expressed in terms of the magnetization and two-spin correlations of the effective model. It is shown that the long-range order is not destroyed by the random field and the transition temperature increases as

{p}_{0}

decreases. For a given

{p}_{0}

the critical temperature increases with the field strength and these combined effects show that the annealed random field favors the ordering of the system, therefore presenting behavior opposite to that expected for the system in a quenched random field.