Statistical Thermodynamics of Finite Ising Model. II

Suzuki, Masuo; Kawabata, Chikao; Ono, Syû; Karaki, Yoshitomo; Ikeda, Masuo

doi:10.1143/jpsj.29.837

Cited by 39 publications

(15 citation statements)

References 16 publications

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“…Accepting that the plot is in fact linear near the origin, and fitting for the slope only gives g(0) = a 1 = 0.0454 (9). Using β 0 = 0.3670 [12,13,14] and ∆e = 2πg(0)(3/2) exp(−3β 0 /2), we find that the corresponding latent heat is ∆e = 0.247(5), comparing well with 0.2409(8) from [12,13] and with 0.2421 (5) from the more sophisticated analysis of [14].…”

Section: D 10-state Potts Modelsupporting

confidence: 74%

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Analysis of the Density of Partition Function Zeroes: A Measure for Phase Transition Strength

Janke

Kenna

2002

Springer Proceedings in Physics

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Abstract. We discuss a numerical analysis employing the density of partition function zeroes which permits effective distinction between phase transitions of first and second order, elucidates crossover between such phase transitions and gives a new way to measure their strengths in the form of latent heat and critical exponents. Application to a number of models demonstrates the efficacy of the technique.A central theme of statistical physics is how best to distinguish between phase transitions of first and second order from simulational data for finite systems [1]. Numerical methods usually exploit the finite-size scaling (FSS) behaviour of thermodynamic quantities exhibiting rounded and shifted peaks whose shape depends on the order and the strength of the transition and which become singular in the thermodynamic limit at the transition point. An alternative strategy is the analysis of the FSS behaviour of partition function zeroes [2,3,4]. For field-driven phase transitions one is interested in the LeeYang zeroes in the plane of complex external magnetic field h [2], and for temperature-driven transitions the Fisher zeroes in the complex temperature plane are relevant [3]. For d-dimensional systems below the upper critical dimension, the FSS behaviour of the j th partition function zero (for large j) is given by [4] Here, L is the system size, η is the anomalous dimension, t = T /T c − 1 is the reduced temperature which is zero in the first formula, and h denotes the external field which is zero in the second formula. The integer index j increases with distance from the critical point. Despite early efforts [5], it has been considered prohibitively difficult if not impossible to extract the density of zeroes from finite lattice data [6]. This problem has resurfaced recently as zeroes-related techniques have become more widespread [7]. This provides the motivation for the present work in which we wish to suggest an approach suitable for density analyses.For finite L, the partition function may always be factorized as Z L (z) = A(z) j (z − z j (L)), where z stands generically for an appropriate function of

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Section: D 10-state Potts Modelsupporting

confidence: 74%

“…The integer index j increases with distance from the critical point. Despite early efforts [5], it has been considered prohibitively difficult if not impossible to extract the density of zeroes from finite lattice data [6]. This problem has resurfaced recently as zeroes-related techniques have become more widespread [7].…”

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confidence: 99%

Analysis of the Density of Partition Function Zeroes: A Measure for Phase Transition Strength

Janke

Kenna

2002

Springer Proceedings in Physics

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“…Lee and Yang [17] also formulated the celebrated circle theorem which states that the partition function zeros of the Ising ferromagnet lie on the unit circle in the complex magnetic-field (X = e βH ) plane. In three dimensions the properties of the zeros in the complex X plane of the Ising model have been studied by exact enumeration [22] and series expansion [23].…”

Section: Introductionmentioning

confidence: 99%

Partition function zeros of the Q-state Potts model on the simple-cubic lattice

Kim

2002

Nuclear Physics B

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The Q-state Potts model on the simple-cubic lattice is studied using the zeros of the exact partition function on a finite lattice. The critical behavior of the model in the ferromagnetic and antiferromagnetic phases is discussed based on the distribution of the zeros in the complex temperature plane. The characteristic exponents at complex-temperature singularities, which coexist with the physical critical points in the complex temperature plane for no magnetic field (H q = 0), are estimated using the low-temperature series expansion. We also study the partition function zeros of the Potts model for nonzero magnetic field. For H q > 0 the physical critical points disappear and the Fisher edge singularities appear in the complex temperature plane. The characteristic exponents at the Fisher edge singularities are calculated using the high-field, low-temperature series expansion. It seems that the Fisher edge singularity is related to the Yang-Lee edge singularity which appears in the complex magnetic-field plane for T > T c .

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“…On the one hand, there are straightforward solutions of Z͑z͒ 0 for dimensions D $ 2 which are, however, restricted to systems of a few interacting spins only [4][5][6][7]. On the other hand, the basic relation [1],…”

Section: Angewandte Physik Gerhard-mercator-universität Duisburg D-mentioning

confidence: 99%

Density of Zeros on the Lee-Yang Circle Obtained from Magnetization Data of a Two-Dimensional Ising Ferromagnet

Binek¹

1998

Phys. Rev. Lett.

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Statistical Thermodynamics of Finite Ising Model. II

Cited by 39 publications

References 16 publications

Analysis of the Density of Partition Function Zeroes: A Measure for Phase Transition Strength

Analysis of the Density of Partition Function Zeroes: A Measure for Phase Transition Strength

Partition function zeros of the Q-state Potts model on the simple-cubic lattice

Density of Zeros on the Lee-Yang Circle Obtained from Magnetization Data of a Two-Dimensional Ising Ferromagnet

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