# Replica theory of the random spherical interface

## Abstract

We investigate the thermodynamics of a spherical interface with quenched disorder in {ital D} spatial dimensions, using the variational replica approach of M{acute e}zard and Parisi. While the disorder-free system exhibits a continuous phase transition analogous to Bose condensation for D{ge}3, arbitrarily weak disorder removes this transition in three and four dimensions. For D{le}4 there is a critical value of the mean square wandering of the interface, below which there is no breaking of replica symmetry, and above which the replica symmetry is spontaneously broken at a finite temperature. Replica symmetry breaking is discontinuous, but the one step solution is found to be unstable. We also calculate the helicity modulus of the interface and show that for any {ital D} it is equal to that of the pure system at the same temperature and chemical potential. {copyright} {ital 1999} {ital The American Physical Society}

- Authors:

- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 686449

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, B: Condensed Matter

- Additional Journal Information:
- Journal Volume: 60; Journal Issue: 10; Other Information: PBD: Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; THERMODYNAMICS; SPHERES; INTERFACES; RANDOMNESS; PHASE TRANSFORMATIONS; REPLICA TECHNIQUES; SYMMETRY BREAKING; HELICITY; BOSE-EINSTEIN CONDENSATION

### Citation Formats

```
Sasik, R.
```*Replica theory of the random spherical interface*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevB.60.7196.

```
Sasik, R.
```*Replica theory of the random spherical interface*. United States. doi:10.1103/PhysRevB.60.7196.

```
Sasik, R. Wed .
"Replica theory of the random spherical interface". United States. doi:10.1103/PhysRevB.60.7196.
```

```
@article{osti_686449,
```

title = {Replica theory of the random spherical interface},

author = {Sasik, R.},

abstractNote = {We investigate the thermodynamics of a spherical interface with quenched disorder in {ital D} spatial dimensions, using the variational replica approach of M{acute e}zard and Parisi. While the disorder-free system exhibits a continuous phase transition analogous to Bose condensation for D{ge}3, arbitrarily weak disorder removes this transition in three and four dimensions. For D{le}4 there is a critical value of the mean square wandering of the interface, below which there is no breaking of replica symmetry, and above which the replica symmetry is spontaneously broken at a finite temperature. Replica symmetry breaking is discontinuous, but the one step solution is found to be unstable. We also calculate the helicity modulus of the interface and show that for any {ital D} it is equal to that of the pure system at the same temperature and chemical potential. {copyright} {ital 1999} {ital The American Physical Society}},

doi = {10.1103/PhysRevB.60.7196},

journal = {Physical Review, B: Condensed Matter},

number = 10,

volume = 60,

place = {United States},

year = {1999},

month = {9}

}