Using thermodynamic fluctuation theory, we study the finite-size rounding of anomalies occurring at first-order phase transitions of the corresponding infinite system. Explicit expressions for thermodynamic functions are derived both for "symmetric transitions" (such as the jump of the spontaneous magnetization in the Ising model from $+{M}_{\mathrm{sp}}$ to $\ensuremath{-}{M}_{\mathrm{sp}}$ as the field changes from ${0}^{+}$ to ${0}^{\ensuremath{-}}$) as well as for asymmetric cases, but restricting attention to (hyper)cubic system shapes. As an explicit example for the usefulness of these considerations in Monte Carlo simulations where it may be a problem to (i) locate a phase transition and (ii) distinguish first-order from second-order transitions, we present numerical results for the two-dimensional nearest-neighbor Ising ferromagnet in a field, both below the critical temperature ${T}_{c}$ and at ${T}_{c}$ . The numerical results are found to be in very good agreement with the phenomenological theory and it is shown that one may extract the magnitudes of jumps occurring at first-order phase transitions in a well-defined and accurate way.Using thermodynamic fluctuation theory, we study the finite-size rounding of anomalies occurring at first-order phase transitions of the corresponding infinite system. Explicit expressions for thermodynamic functions are derived both for "symmetric transitions" (such as the jump of the spontaneous magnetization in the Ising model from $+{M}_{\mathrm{sp}}$ to $\ensuremath{-}{M}_{\mathrm{sp}}$ as the field changes from ${0}^{+}$ to ${0}^{\ensuremath{-}}$) as well as for asymmetric cases, but restricting attention to (hyper)cubic system shapes. As an explicit example for the usefulness of these considerations in Monte Carlo simulations where it may be a problem to (i) locate a phase transition and (ii) distinguish first-order from second-order transitions, we present numerical results for the two-dimensional nearest-neighbor Ising ferromagnet in a field, both below the critical temperature ${T}_{c}$ and at ${T}_{c}$. The numerical results are found to be in very good agreement with the phenomenological theory and it is shown that one may extract the magnitudes of jumps occurring at first-order phase transitions in a well-defined and accurate way.

Physical review. B, Condensed matterAug 1, 1984634 citations

First-order phase transition in $1d$ Potts model with long-range interactionsFirst-order phase transition in $1d$ Potts model with long-range interactions

Katarina Uzelac, Zvonko Glumac

The first-order phase transition in the one-dimensional $q$ -state Potts model with long-range interactions decaying with distance as $1/r^{1+σ}$ has been studied by Monte Carlo numerical simulations for $0 < σ\le 1$ and integer values of $q > 2$ . On the basis of finite-size scaling analysis of interface free energy $ΔF_L$ , specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for $σ$ below a threshold value $σ_c(q)$ .The first-order phase transition in the one-dimensional $q$-state Potts model with long-range interactions decaying with distance as $1/r^{1+σ}$ has been studied by Monte Carlo numerical simulations for $0 < σ\le 1$ and integer values of $q > 2$. On the basis of finite-size scaling analysis of interface free energy $ΔF_L$, specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for $σ$ below a threshold value $σ_c(q)$.

arXiv:cond-mat/9807416Fizika BJul 31, 19983 citations

Numerical investigations of phase transitions and critical phenomena

M I Tribel'skiĭ

Soviet Physics UspekhiJan 31, 19880 citations

+{M}_{\mathrm{sp}}

to $\ensuremath{-}{M}_{\mathrm{sp}}$ as the field changes from

{0}^{+}

to ${0}^{\ensuremath{-}}$) as well as for asymmetric cases, but restricting attention to (hyper)cubic system shapes. As an explicit example for the usefulness of these considerations in Monte Carlo simulations where it may be a problem to (i) locate a phase transition and (ii) distinguish first-order from second-order transitions, we present numerical results for the two-dimensional nearest-neighbor Ising ferromagnet in a field, both below the critical temperature

{T}_{c}

and at

{T}_{c}

. The numerical results are found to be in very good agreement with the phenomenological theory and it is shown that one may extract the magnitudes of jumps occurring at first-order phase transitions in a well-defined and accurate way.

First-order phase transition in

1d

Potts model with long-range interactions

The first-order phase transition in the one-dimensional

q

-state Potts model with long-range interactions decaying with distance as

1/r^{1+σ}

has been studied by Monte Carlo numerical simulations for

0 < σ\le 1

and integer values of

q > 2

. On the basis of finite-size scaling analysis of interface free energy

ΔF_L

, specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for

σ

below a threshold value

σ_c(q)