# Critical exponent for the density of percolating flux

## Abstract

This paper is a study of some of the critical properties of a simple model for flux. The model is motivated by SU(2) gauge theory at nonzero temperature and is equivalent to the Ising model in three dimensions. The phase with condensed flux is studied. This is the ordered phase of the Ising model and the high temperature, deconfined phase of the gauge theory. The flux picture will be used in this phase. Near the transition, the density of flux is low enough so that flux variables remain useful. There is a finite density of finite flux clusters on both sides of the phase transition. In the deconfined phase, there is also an infinite, percolating network of flux with a density that vanishes as {ital T}{r_arrow}{ital T}{sub {ital c}}{sup +}. On both sides of the critical point, the nonanalyticity in the total flux density is characterized by the exponent (1{minus}{alpha}). The main result of this paper is a calculation of the critical exponent for the percolating network. The exponent for the density of the percolating cluster is {zeta}=(1{minus}{alpha}){minus}({ital cphi}{minus}1). The specific heat exponent {alpha} and the crossover exponent {ital cphi} can be computed in the {epsilon} expansion. Since {zeta}{lt}(1{minus}{alpha}), themore »

- Authors:

- Department of Physics, University of California, Davis, California 95616 (United States)

- Publication Date:

- OSTI Identifier:
- 142735

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D

- Additional Journal Information:
- Journal Volume: 49; Journal Issue: 5; Other Information: PBD: 1 Mar 1994

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; FLUX DENSITY; CRITICALITY; SU-2 GROUPS; UNIFIED GAUGE MODELS; ISING MODEL; PHASE TRANSFORMATIONS; SPECIFIC HEAT

### Citation Formats

```
Kiskis, J.
```*Critical exponent for the density of percolating flux*. United States: N. p., 1994.
Web. doi:10.1103/PhysRevD.49.2597.

```
Kiskis, J.
```*Critical exponent for the density of percolating flux*. United States. doi:10.1103/PhysRevD.49.2597.

```
Kiskis, J. Tue .
"Critical exponent for the density of percolating flux". United States. doi:10.1103/PhysRevD.49.2597.
```

```
@article{osti_142735,
```

title = {Critical exponent for the density of percolating flux},

author = {Kiskis, J.},

abstractNote = {This paper is a study of some of the critical properties of a simple model for flux. The model is motivated by SU(2) gauge theory at nonzero temperature and is equivalent to the Ising model in three dimensions. The phase with condensed flux is studied. This is the ordered phase of the Ising model and the high temperature, deconfined phase of the gauge theory. The flux picture will be used in this phase. Near the transition, the density of flux is low enough so that flux variables remain useful. There is a finite density of finite flux clusters on both sides of the phase transition. In the deconfined phase, there is also an infinite, percolating network of flux with a density that vanishes as {ital T}{r_arrow}{ital T}{sub {ital c}}{sup +}. On both sides of the critical point, the nonanalyticity in the total flux density is characterized by the exponent (1{minus}{alpha}). The main result of this paper is a calculation of the critical exponent for the percolating network. The exponent for the density of the percolating cluster is {zeta}=(1{minus}{alpha}){minus}({ital cphi}{minus}1). The specific heat exponent {alpha} and the crossover exponent {ital cphi} can be computed in the {epsilon} expansion. Since {zeta}{lt}(1{minus}{alpha}), the variation in the separate densities is much more rapid than that of the total. Flux is moving from the infinite cluster to the finite clusters much more rapidly than the total density is decreasing.},

doi = {10.1103/PhysRevD.49.2597},

journal = {Physical Review, D},

number = 5,

volume = 49,

place = {United States},

year = {1994},

month = {3}

}