### Abstract

We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner-Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two "normal", massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J. Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultraviolet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the "mass corrections". The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J → 0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.

Original language | English |
---|---|

Pages (from-to) | 467-492 |

Number of pages | 26 |

Journal | Nuclear Physics B |

Volume | 725 |

Issue number | 3 |

DOIs | |

Publication status | Published - Oct 10 2005 |

### Fingerprint

### Keywords

- Renormalization
- Renormalization group evolution of parameters

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Renormalization-group analysis of layered sine-Gordon type models.** / Nándori, I.; Nagy, S.; Sailer, K.; Jentschura, U.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 725, no. 3, pp. 467-492. https://doi.org/10.1016/j.nuclphysb.2005.07.016

}

TY - JOUR

T1 - Renormalization-group analysis of layered sine-Gordon type models

AU - Nándori, I.

AU - Nagy, S.

AU - Sailer, K.

AU - Jentschura, U.

PY - 2005/10/10

Y1 - 2005/10/10

N2 - We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner-Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two "normal", massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J. Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultraviolet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the "mass corrections". The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J → 0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.

AB - We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner-Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two "normal", massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J. Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultraviolet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the "mass corrections". The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J → 0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.

KW - Renormalization

KW - Renormalization group evolution of parameters

UR - http://www.scopus.com/inward/record.url?scp=24644518637&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24644518637&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2005.07.016

DO - 10.1016/j.nuclphysb.2005.07.016

M3 - Article

AN - SCOPUS:24644518637

VL - 725

SP - 467

EP - 492

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -