# Random matrix model of QCD at finite density and the nature of the quenched limit

## Abstract

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential {mu}. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive {open_quote}{open_quote}replica trick{close_quote}{close_quote} fails for {mu}{ne}0; we find that quenched QCD is not a simple {ital n}{r_arrow}0 limit of QCD with {ital n} quarks. It is the limit of a theory with 2{ital n} quarks: {ital n} quarks with original action and {ital n} quarks with conjugate action. The results agree with earlier studies of lattice QCD at {mu}{ne}0 and provide a simple analytical explanation of a long-standing puzzle. {copyright} {ital 1996 The American Physical Society.}

- Authors:

- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 (United States)

- Publication Date:

- OSTI Identifier:
- 285755

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 76; Journal Issue: 24; Other Information: PBD: Jun 1996

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; QUANTUM CHROMODYNAMICS; CHIRAL SYMMETRY; SYMMETRY BREAKING; DENSITY; QUENCHING; RANDOMNESS; EIGENVALUES; QUARKS; DIRAC OPERATORS

### Citation Formats

```
Stephanov, M.A..
```*Random matrix model of QCD at finite density and the nature of the quenched limit*. United States: N. p., 1996.
Web. doi:10.1103/PhysRevLett.76.4472.

```
Stephanov, M.A..
```*Random matrix model of QCD at finite density and the nature of the quenched limit*. United States. doi:10.1103/PhysRevLett.76.4472.

```
Stephanov, M.A.. Sat .
"Random matrix model of QCD at finite density and the nature of the quenched limit". United States. doi:10.1103/PhysRevLett.76.4472.
```

```
@article{osti_285755,
```

title = {Random matrix model of QCD at finite density and the nature of the quenched limit},

author = {Stephanov, M.A.},

abstractNote = {We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential {mu}. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive {open_quote}{open_quote}replica trick{close_quote}{close_quote} fails for {mu}{ne}0; we find that quenched QCD is not a simple {ital n}{r_arrow}0 limit of QCD with {ital n} quarks. It is the limit of a theory with 2{ital n} quarks: {ital n} quarks with original action and {ital n} quarks with conjugate action. The results agree with earlier studies of lattice QCD at {mu}{ne}0 and provide a simple analytical explanation of a long-standing puzzle. {copyright} {ital 1996 The American Physical Society.}},

doi = {10.1103/PhysRevLett.76.4472},

journal = {Physical Review Letters},

number = 24,

volume = 76,

place = {United States},

year = {1996},

month = {6}

}

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