Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bond<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>Blume-Capel model

Malakis, A.; Berker, A. Nihat; Hadjiagapiou, Ioannis A.; Fytas, Nikolaos G.; Papakonstantinou, Theodoros

doi:10.1103/physreve.81.041113

Cited by 69 publications

(55 citation statements)

References 82 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In the case of three dimensions, the ferromagnetic (FM) transition still occurs in regimes with weak disorder, while the transition temperature decreases with increasing disorder. Harris [49] pointed out that the sign of the specific heat exponent α 0 in a nonrandom system would be a determinant of the relevance of randomness to the critical universality of the FM transition [50][51][52][53][54][55][56][57][58][59][60][61]. Due to this criterion, since α 0 is negative for the GG model in three dimensions, the weak disorder is irrelevant and the system stays in the same universality class as the nonrandom system.…”

Section: Introductionmentioning

confidence: 99%

Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

et al. 2014

View full text Add to dashboard Cite

The critical exponents are estimated for the gauge glass model in two dimensions, in which only the Kosterlitz-Thouless (KT) phase appears in the low-temperature regime. The nonequilibrium relaxation method is applied to estimate the transition temperature and critical exponents: the static exponent η and the dynamical exponent z. Since the system exhibits criticality in the whole KT phase, we estimate the exponents on the boundary as well as inside the KT phase. The static exponent η depends on both the temperature and the strength of randomness, while the dynamical one z is almost constant throughout the KT phase, including the boundary.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Several recent studies propose improvements and sophisticated implementations of the WL algorithm [4][5][6][7][8][9][10][11][12][13][14]. A controversial point in the application of the WL and related methods is the saturation of the error, i.e., the difference between the simulation estimate for g(E) and the exact values.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic convergence properties of entropic sampling algorithms

Belardinelli¹,

Pereyra²,

Dickman³

et al. 2014

J. Stat. Mech.

View full text Add to dashboard Cite

We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang-Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f → f /2) each time the flat-histogram condition is satisfied, in the second f ∼ 1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time).To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E = 1, ..., L, there is exactly one state, that is, g(E) = 1 for all E. Convergence of sampling corresponds to g(E, t) → const. as t → ∞, so that the standard deviation σ g of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases σ g saturates at long times. In the 1/t algorithm, by contrast, σ g decays ∝ 1/ √ t. Modified TS and 1/t procedures, in which f ∝ 1/t α , converge for α values between 0 < α ≤ 1. There are two essential facets to convergence of flat-histogram methods:elimination of initial errors in g(E), and correction of the sampling noise accumulated during the process. For a simple example, we demonstrate analytically, using a Langevin equation, that both kinds of errors can be eliminated, asymptotically, if f ∼ 1/t α with 0 < α ≤ 1.Convergence is optimal for α = 1. For α ≤ 0 the sampling noise never decays, while for α > 1 the initial error is never completely eliminated.

show abstract

“…Furthermore, It is a characterization for the experimental 3He-4He mixtures [9,10] and metamagnets [11], which inspired the vector version of this model [12,13]. The introduction of the bond randomness [14,15] enriches the phase transition discussions about this model.…”

mentioning

confidence: 99%

Tensor Renormalization Group Study of the General Spin-S Blume–Capel Model

Yang

Xie

2016

J. Phys. Soc. Jpn.

View full text Add to dashboard Cite

We focus on the special situation of D = 2J of the general spin-S Blume-Capel model on the square lattice. Under the infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are discussed by the newly developed tensor renormalization group method. For the case of the integer spin-S, the system will undergo S first-order phase transitions with the successive symmetry breaking with the magnetization M = S, S − 1, ...0. For the half-integer spin-S, there are similar S − 1/2 first order phase transition with M = S, S − 1, ...1/2 stepwise structure, in addition, there is a continuous phase transition due to the spin-flip Z2 symmetry breaking. In the low temperature regions, all first-order phase transitions are accompanied by the successive disappearance of the optional spin-component pairs(s, −s), furthermore, the critical temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of the magnetic field, the visualization parameter characterizing the intrinsic degeneracy of the different phases clearly demonstrates the phase transition process. where the spin variable S takes 2S + 1 values: (−S, −S + 1, ..., S − 1, S). J is the coupling constant, D is the strength of the single-ion anisotropy and h is the magnetic field. The sum of the first term runs over all the nearest neighbors. Firstly, we consider the case of h = 0. When D = 0, this model is reduced to the classical Ising model. When D goes to the positive infinity, the energy favorable state is the one with the full occupation of the smallest spin component. For the integer spin cases, the component is S = 0. For the half-integer cases, the component is S = ±1/2. If we look at the hamiltonian of any bond linking two * Electronic address: liping2012@cqu.edu.cn sites i, j, then we haveHere, q is the coordination number depending on the lattice structure. This formula can be rewritten asfrom which, it leads to the following conclusions for the ferromagnetic coupling(J > 0): when D > qJ/2, the configuration of the ground state is S i = S j = 0, S i = S j = 1/2(−1/2)(depending on the spontaneous breaking), respectively for the integer and half-odd spin-S cases; when D < qJ/2, the configuration of the ground state is S i = S j = max(S) for any spin-S cases. As a result, we have a special situation, i.e., D = qJ/2, where the ground state is S i = S j with (2S + 1)-fold degeneracy. Once the magnetic field h is turned on as a smallness, the ground state degeneracy is lifted in the case of D = qJ/2. The positive smallness h make the system go into the ground state S i = S j = max(S) as the case D < qJ/2 with h = 0. Without loss of the generality, we focus on the square lattice hereafter. Then, q = 4 and D = 2J is the special parameter. The phase boundaries of the square lattice [3,4,6,8] end at (T /J, D/J) = (0, 2), i.e., for D = 2J, and the critical temperature is T c = 0 for the general spin cases when h = 0.Motivated by the special parameter point and the though...

show abstract

Multicritical points and crossover mediating the strong violation of universality: Wang-Landau determinations in the random-bondd=2Blume-Capel model

Cited by 69 publications

References 82 publications

Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

Intrinsic convergence properties of entropic sampling algorithms

Tensor Renormalization Group Study of the General Spin-S Blume–Capel Model

Contact Info

Product

Resources

About