Helmholtz free energy of finite spin systems near criticality

Eisenriegler, E.; Tomaschitz, Roman

doi:10.1103/physrevb.35.4876

Cited by 37 publications

(31 citation statements)

References 32 publications

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“…The Wolff algorithm was adapted to take into account the anisotropies of the model, according to the prescription described by Ala-Nissila [22] and also the dimensionality of the lattice. A simple cubic lattice with periodic boundary conditions was used with system sizes L = 16,18,20,22,24,30,34,40,44, and very long runs were performed, ranging from 280 million to 1.5 billion hybrid Monte Carlo steps (HMCS) so as to achieve good precision, specially on the calculation of cumulants. We also extended the analysis for L = 60, 64, and 70 for reasons that will be clear below.…”

Section: Resultsmentioning

confidence: 99%

“…Based on finite-size scaling arguments, analogous to usual finite-size scaling assumptions [6,16], it is expected that, at criticality and large enough system sizes L, the order parameter probability distribution P(m) should obey the following scaling relation [6]:…”

Section: A Universal Probability Distribution Functionsmentioning

confidence: 99%

“…Bearing in mind that, near criticality, the singular part f s of the free energy is a generalized homogeneous function of its parameters [17] and Kadanoff's seminal renormalization group ideas [16,18], one can write for the ^-dimensional Ising model…”

Section: A Universal Probability Distribution Functionsmentioning

confidence: 99%

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Bicritical universality of the anisotropic Heisenberg model in a crystal field

Freire

Plascak

2015

Phys. Rev. E

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The bicritical properties of the three-dimensional classical anisotropic Heisenberg model in a crystal field are investigated through extensive Monte Carlo simulations on a simple cubic lattice, using Metropolis and Wolff algorithms. Field-mixing and multidimensional histogram techniques were employed in order to compute the probability distribution function of the extensive conjugate variables of interest and, using finite-size scaling analysis, the first-order transition line of the model was precisely located. The fourth-order cumulant of the order parameter was then calculated along this line and the bicritical point located with good precision from the cumulant crossings. The bicritical properties of this point were further investigated through the measurement of the universal probability distribution function of the order parameter. The results lead us to conclude that the studied bicritical point belongs in fact to the three-dimensional Heisenberg universality class.

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Section: Resultsmentioning

confidence: 99%

Section: A Universal Probability Distribution Functionsmentioning

confidence: 99%

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Bicritical universality of the anisotropic Heisenberg model in a crystal field

Freire

Plascak

2015

Phys. Rev. E

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“…Moreover, a double-peak behaviour in the distribution of the order parameter may be misleading [12].…”

Section: Model and The Methodsmentioning

confidence: 99%

Study of cluster fluctuations in the two-dimensional q-state Potts model

Aydın¹,

Gündüç²,

Çelik³

1996

Physica A: Statistical Mechanics and its Applications

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The two-dimensional Potts Model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.

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“…Most applications of these theories to three-dimensional systems have been restricted to T higher than the bulk critical temperature T C [13] with a few calculations in region below T C [14]. However, some limitations exist in the theories of [11] and [12].…”

Section: Local Spontaneous Symmetry Breaking For Finite-size Systemmentioning

confidence: 99%

Perturbative calculation of the scaled factorial moments in the second-order quark-hadron phase transition within the Ginzburg-Landau description

Yang

Cai

1999

Phys. Rev. C

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The scaled factorial moments Fq are studied for a second-order quark-hadron phase transition within the Ginzburg-Landau description. The role played by the ground state of the system under low temperature is emphasized. After a local shift of the order parameter the fluctuations are around the ground state, and a perturbative calculation for Fq can be carried out. Power scaling between Fq's is shown, and a universal scaling exponent ν ≃ 1.75 is given for the case with weak correlations and weak self-interactions.

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Helmholtz free energy of finite spin systems near criticality

Cited by 37 publications

References 32 publications

Bicritical universality of the anisotropic Heisenberg model in a crystal field

Bicritical universality of the anisotropic Heisenberg model in a crystal field

Study of cluster fluctuations in the two-dimensional q-state Potts model

Perturbative calculation of the scaled factorial moments in the second-order quark-hadron phase transition within the Ginzburg-Landau description

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