# Method for simulating O(N) lattice models at finite density

## Abstract

We present a method for simulating relativistic and nonrelativistic scalar field theories at finite density, with matter transforming in the fundamental representation of the global symmetry group O(N). The method avoids the problem of complex probability weights which is present in conventional path integral Monte Carlo algorithms. To verify our approach, we simulate the free and interacting relativistic U(1){approx_equal}O(2) theory in 2+1 dimensions. We compute the two-point correlation function and charge density as a function of chemical potential in the free theory. At weak |{phi}|{sup 4} coupling and zero temperature we map the m{sup 2}-{mu} phase diagram and compare our numerical results with perturbative calculations. Finally, we compute properties of the T-{mu} phase diagram in the vicinity of the phase transition and at bare self-couplings large compared to the temperature and chemical potential.

- Authors:

- Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195-1550 (United States)

- Publication Date:

- OSTI Identifier:
- 21020191

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.065012; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; CHARGE DENSITY; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CORRELATION FUNCTIONS; COUPLING; MONTE CARLO METHOD; O GROUPS; PATH INTEGRALS; PHASE DIAGRAMS; PHASE TRANSFORMATIONS; POTENTIALS; QUANTUM FIELD THEORY; RELATIVISTIC RANGE; SCALAR FIELDS; SYMMETRY GROUPS; U-1 GROUPS

### Citation Formats

```
Endres, Michael G.
```*Method for simulating O(N) lattice models at finite density*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.065012.

```
Endres, Michael G.
```*Method for simulating O(N) lattice models at finite density*. United States. doi:10.1103/PHYSREVD.75.065012.

```
Endres, Michael G. Thu .
"Method for simulating O(N) lattice models at finite density". United States.
doi:10.1103/PHYSREVD.75.065012.
```

```
@article{osti_21020191,
```

title = {Method for simulating O(N) lattice models at finite density},

author = {Endres, Michael G.},

abstractNote = {We present a method for simulating relativistic and nonrelativistic scalar field theories at finite density, with matter transforming in the fundamental representation of the global symmetry group O(N). The method avoids the problem of complex probability weights which is present in conventional path integral Monte Carlo algorithms. To verify our approach, we simulate the free and interacting relativistic U(1){approx_equal}O(2) theory in 2+1 dimensions. We compute the two-point correlation function and charge density as a function of chemical potential in the free theory. At weak |{phi}|{sup 4} coupling and zero temperature we map the m{sup 2}-{mu} phase diagram and compare our numerical results with perturbative calculations. Finally, we compute properties of the T-{mu} phase diagram in the vicinity of the phase transition and at bare self-couplings large compared to the temperature and chemical potential.},

doi = {10.1103/PHYSREVD.75.065012},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}