Moment-generating function zeros in the study of phase transitions

Rodrigues, R. G. M.; Costa, B. V.; Mól, L. A. S.

doi:10.1103/physreve.104.064103

Cited by 5 publications

(3 citation statements)

References 30 publications

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“…The first part, Z < , includes energies E < E ′ , Z ′ covers the energy range of the non-stable region [E ′ , E ′′ ] (as discussed in section 2.1), and Z> accounts for energies E > E ′ ′ . It can be claimed that Z ′ (B = B j ) ≈ 0 since approaches that truncate the energy range, such as the zeros of the DOS [15][16][17], can capture the indications of phase transitions. Thus, we have:…”

Section: Fisher Zeros For a First-order Phase Transitionmentioning

confidence: 99%

Connecting the unstable region of the entropy to the pattern of the Fisher zeros map

Rocha,

Costa

2024

J. Stat. Mech.

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Phase transitions are one of the most interesting natural phenomena. For finite systems, one of the concerns in the topic is how to classify a specific transition as a being of first, second, or even of a higher order according to the Ehrenfest classification. The partition function provides all the thermodynamic information about the physical systems, and a phase transition can be identified using the complex temperature where it is equal to zero. In addition, the pattern of zeros in the complex temperature plane can provide evidence of the transition order. This manuscript presents an analytical and simulational study connecting the microcanonical analysis of the unstable region of the entropy to the canonical partition function zeros. We show that, for the first-order transition, the zeros accumulate uniformly in a vertical line on the complex inverse temperature plane as discussed in previous works. We illustrate our calculations using a 147 particles Lennard-Jones cluster.

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Section: Fisher Zeros For a First-order Phase Transitionmentioning

confidence: 99%

Connecting the unstable region of the entropy to the pattern of the Fisher zeros map

Rocha,

Costa

2024

J. Stat. Mech.

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“…The EPD method to determine the dominant zero was developed in reference [3][4][5]. It consists in judiciously selecting the most relevant zeros for a chosen temperature in the following way.…”

Section: Energy Probability Distribution Zeros (Epd)mentioning

confidence: 99%

“…Although we do not have a rigorous demonstration of equation 9, numerical works strongly suggests it holds [3][4][5]. Using the FSS equations above, the critical temperature and exponents can be easily obtained from the simulation data.…”

Section: Finite-size Scalingmentioning

confidence: 99%

Using the Energy probability distribution zeros to obtain the critical properties of the two-dimensional anisotropic Heisenberg model

Souza¹,

Costa²

2022

Preprint

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In this paper we present a Monte Carlo study of the critical behavior of the easy axis anisotropic Heisenberg spin model in two dimensions. Based on the partial knowledge of the zeros of the energy probability distribution we determine with good precision the phase diagram of the model obtaining the critical temperature and exponents for several values of the anisotropy. Our results indicate that the model is in the Ising universality class for any anisotropy.

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Using the Energy Probability Distribution Zeros to Obtain the Critical Properties of the Two-Dimensional Anisotropic Heisenberg Model

Souza

Costa

2022

Braz J Phys

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Moment-generating function zeros in the study of phase transitions

Cited by 5 publications

References 30 publications

Connecting the unstable region of the entropy to the pattern of the Fisher zeros map

Connecting the unstable region of the entropy to the pattern of the Fisher zeros map

Using the Energy probability distribution zeros to obtain the critical properties of the two-dimensional anisotropic Heisenberg model

Using the Energy Probability Distribution Zeros to Obtain the Critical Properties of the Two-Dimensional Anisotropic Heisenberg Model

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