# Criticality and crossover in accessible regimes

## Abstract

The near-critical behavior of (d=3)-dimensional Ising-model ferromagnets or simple lattice gases with equivalent first, second, and third nearest-neighbor interactions is studied through Monte Carlo simulations using histogram reweighting techniques and comparisons with series expansions. By carefully analyzing numerical data from relatively small finite systems using scaling and extrapolation methods, it is demonstrated that one can reliably estimate critical exponents, critical temperatures, and universal amplitude ratios, thereby distinguishing convincingly between different ''nearby'' universality classes and revealing systematic crossover effects. This study is preparatory to extending similar techniques to study criticality in continuum fluid models lacking symmetries, with Coulomb interactions, etc. (c) 2000 The American Physical Society.

- Authors:

- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2431 (United States)

- Publication Date:

- OSTI Identifier:
- 20216397

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 5; Other Information: PBD: May 2000; Journal ID: ISSN 1063-651X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FERROMAGNETIC MATERIALS; CRITICAL TEMPERATURE; MONTE CARLO METHOD; SCALING LAWS; PHASE TRANSFORMATIONS; THEORETICAL DATA

### Citation Formats

```
Orkoulas, G., Panagiotopoulos, A. Z., and Fisher, Michael E.
```*Criticality and crossover in accessible regimes*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevE.61.5930.

```
Orkoulas, G., Panagiotopoulos, A. Z., & Fisher, Michael E.
```*Criticality and crossover in accessible regimes*. United States. doi:10.1103/PhysRevE.61.5930.

```
Orkoulas, G., Panagiotopoulos, A. Z., and Fisher, Michael E. Mon .
"Criticality and crossover in accessible regimes". United States. doi:10.1103/PhysRevE.61.5930.
```

```
@article{osti_20216397,
```

title = {Criticality and crossover in accessible regimes},

author = {Orkoulas, G. and Panagiotopoulos, A. Z. and Fisher, Michael E.},

abstractNote = {The near-critical behavior of (d=3)-dimensional Ising-model ferromagnets or simple lattice gases with equivalent first, second, and third nearest-neighbor interactions is studied through Monte Carlo simulations using histogram reweighting techniques and comparisons with series expansions. By carefully analyzing numerical data from relatively small finite systems using scaling and extrapolation methods, it is demonstrated that one can reliably estimate critical exponents, critical temperatures, and universal amplitude ratios, thereby distinguishing convincingly between different ''nearby'' universality classes and revealing systematic crossover effects. This study is preparatory to extending similar techniques to study criticality in continuum fluid models lacking symmetries, with Coulomb interactions, etc. (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevE.61.5930},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

issn = {1063-651X},

number = 5,

volume = 61,

place = {United States},

year = {2000},

month = {5}

}