Critical exponents of a three-dimensional weakly diluted quenched Ising model

Folk, R.; Holovatch, Yu.; Yavors’kii, T.

doi:10.3367/ufnr.0173.200302c.0175

Cited by 81 publications

(95 citation statements)

References 138 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The quest for a determination of the properties of the expected random fixed point in the 3D disordered Ising model is already rather long. A comprehensive compilation of results can be found in (Folk et al, 2000(Folk et al, , 2003 and , showing a wide scatter in the critical exponents of different groups, presumably due to large crossover effects. Recent MC simulations (Ballesteros et al, 1998a;Berche et al, 2005Berche et al, , 2004Ivaneyko et al, 2005) provide evidence for the random fixed point but also show large crossover effects due to the interference with the pure fixed point for p → 0 and with the percolation fixed point for p → p c (recall the discussion in Sect.…”

Section: Three Dimensionsmentioning

confidence: 99%

High-temperature series for the bond-diluted Ising model in 3, 4, and 5 dimensions

Hellmund

Janke

2006

Phys. Rev. B

View full text Add to dashboard Cite

In order to study the influence of quenched disorder on second-order phase transitions, hightemperature series expansions of the susceptibility and the free energy are obtained for the quenched bond-diluted Ising model in d = 3-5 dimensions. They are analysed using different extrapolation methods tailored to the expected singularity behaviours. In d = 4 and 5 dimensions we confirm that the critical behaviour is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in d = 4 is confirmed and our results for the critical behaviour of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation and random fixed point. We estimate the critical exponent of the susceptibility to be γ = 1.305 (5)

show abstract

Section: Three Dimensionsmentioning

confidence: 99%

High-temperature series for the bond-diluted Ising model in 3, 4, and 5 dimensions

Hellmund

Janke

2006

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Already this phenomenon called for its explanation and verification. We refer the reader to recent reviews [2,3] where theoretical, experimental and computational data are collected and compared. In our study, we use the Monte Carlo (MC) approach and address the comparison of three different simulational techniques analysing critical behaviour of the 3D quenched diluted Ising model.…”

Section: Introductionmentioning

confidence: 99%

Criticality of the random-site Ising model: Metropolis, Swendsen-Wang and Wolff Monte Carlo algorithms

Ivaneyko¹,

Ilnytskyi²,

Berche³

et al. 2005

Condens. Matter Phys.

Self Cite

View full text Add to dashboard Cite

We apply numerical simulations to study of the criticality of the 3D Ising model with random site quenched dilution. The emphasis is given to the issues not being discussed in detail before. In particular, we attempt a comparison of different Monte Carlo techniques, discussing regions of their applicability and advantages/disadvantages depending on the aim of a particular simulation set. Moreover, besides evaluation of the critical indices we estimate the universal ratio Γ + /Γ − for the magnetic susceptibility critical amplitudes. Our estimate Γ + /Γ − = 1.67±0.15 is in a good agreement with the recent MC analysis of the random-bond Ising model giving further support that both random-site and random-bond dilutions lead to the same universality class.

show abstract

“…Now it is well established that ν depends on the system universality class (see, for example, [1,2]) and dimensionality. For Ising model, which is considered below, this value also depends on the spin component dilution (replacing magnetic atoms by nonmagnetic ones) and on the type of the impurity distribution [3,4]. In contrast to the ν the quantity ξ 0t is nonuniversal and depends on the microscopic parameters of the system.…”

mentioning

confidence: 99%

“…It depends on the symmetry of the system, on the presence of impurities, etc. [4]. The expression (4) is the consequence of the temperature and field dependence of the system exit point n p on the order parameter critical fluctuations [10].…”

mentioning

confidence: 99%

The effect of finite size of the system on correlation length behaviour at the presence of external field

Kozlovskii¹

2007

Condens. Matter Phys.

View full text Add to dashboard Cite

The explicit analytical expression for the effective correlation length ξ as a function of reduced temperature τ , external field h and system size L for the Ising-like system near the phase transition point Tc is obtained. The role of these quantities in the formation of the correlation length value is ascertained. It is shown that the irregular increase of the correlation length exists only in the case of τ → 0, h → 0 and L → ∞. With deviation from these values the essential slowing down exists for the increasing ξ. The criterium of the permissible range of temperature values (field values), where the correlation length behaviour is defined by temperature (or field) variable, is established for the fixed size of the system. Beyond this range τ < τc, h < hcr the system size becomes crucial for forming the correlation length.Key words: phase transition, correlation length, external field, finite size system PACS: 05.50.+q, 64.60.Fr, 75.10.Hk The correlation length ξ is one of the most important characteristics of the phase transition. This quantity tends to infinity with nearing to the phase transition temperature T c from exponentialat the absence of the external field for infinite systems (τ = (T − T c )/T c ). The quantity ξ 0t is called critical amplitude, and ν is (temperature) critical exponent. Now it is well established that ν depends on the system universality class (see, for example, [1,2]) and dimensionality. For Ising model, which is considered below, this value also depends on the spin component dilution (replacing magnetic atoms by nonmagnetic ones) and on the type of the impurity distribution [3,4]. In contrast to the ν the quantity ξ 0t is nonuniversal and depends on the microscopic parameters of the system. Far from the phase transition point, the quantity ξ 0t takes on the values of the order of the distance between the system particles. The value of the exponent ν as well as other critical exponents for Ising model are known with high accuracy (see, for example, [5]). These are the so-called temperature critical exponents. In addition, the field exponents that describe the dependence of the physical quantities on the field in the case of T = T c , are known as well. Since for the correlation length ξ we have the dependencewhere µ is the (filed) critical exponent of the correlation length at T = T c , ξ 0h is the corresponding critical amplitude , h = βH (H is magnetic field β −1 = kT ). Generalizing different calculation methods ( -series expansion [6], theoretical field approach for fixed dimensionality d = 3 [7], Monte-Carlo calculation data, [8], high-temperature expansions [9]), one may claim that for Ising model ν = 0.630, and µ is determined using the relations for critical exponents µ = ν β + γ .Taking into account the results of papers [6-9], we find µ = 0.402.c M.P.Kozlovskii 173

show abstract

Critical exponents of a three-dimensional weakly diluted quenched Ising model

Cited by 81 publications

References 138 publications

High-temperature series for the bond-diluted Ising model in 3, 4, and 5 dimensions

High-temperature series for the bond-diluted Ising model in 3, 4, and 5 dimensions

Criticality of the random-site Ising model: Metropolis, Swendsen-Wang and Wolff Monte Carlo algorithms

The effect of finite size of the system on correlation length behaviour at the presence of external field

Contact Info

Product

Resources

About