Scale-breaking model of the renormalization group

R Gersch, J Reiss, Carsten Honerkamp A

First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here, we introduce a counterterm technique within the functional renormalization-group (fRG) formalism which allows access to all stable and metastable configurations. It becomes possible to study symmetry-broken states which occur through first-order transitions as well as hysteresis phenomena. For continuous transitions, the standard results are reproduced. As an example, we study discrete-symmetry breaking in a mean-field model for a commensurate charge-density wave. An additional benefit of the approach is that away from the critical temperature for the breaking of discrete symmetries large interactions can be avoided at all RG scales.

Silvio R. A. Salinas

Harukuni Ikeda, Hiroyoshi Nakano

We study the critical behavior of the O(n) O ( n ) model under steady shear flow using a dynamical renormalization group (RG) method. Incorporating the strong anisotropy in scaling ansatz, which has been neglected in earlier RG analyses, we identify a new stable Gaussian fixed point. This fixed point reproduces the anisotropic scaling of static and dynamical critical exponents for both non-conserved (Model A) and conserved (Model B) order parameters. Notably, the upper critical dimensions are d_{\text{up}} = 2 d up = 2 for the non-conserved order parameter (Model A) and d_{\text{up}} = 0 d up = 0 for the conserved order parameter (Model B), implying that the mean-field critical exponents are observed even in both d=2 d = 2 and 3 3 dimensions. Furthermore, the scaling exponent of the order parameter is negative for all dimensions d ≥ 2 d ≥ 2 , indicating that shear flow stabilizes the long-range order associated with continuous symmetry breaking even in d = 2 d = 2 . In other words, the lower critical dimensions are d_{\rm low} < 2 for both types of order parameters. This contrasts with equilibrium systems, where the Hohenberg—Mermin—Wagner theorem prohibits continuous symmetry breaking in d = 2 d = 2 .

Eduardo Fradkin

Belal Ehsan Baaquie

Gersch, R., Reiss, J., Carsten Honerkamp A

First-order phase transitions in many-fermion systems are not detected\n in the susceptibility analysis of common renormalization-group (RG)\n approaches. Here, we introduce a counterterm technique within the\n functional renormalization-group (fRG) formalism which allows access to\n all stable and metastable configurations. It becomes possible to study\n symmetry-broken states which occur through first-order transitions as\n well as hysteresis phenomena. For continuous transitions, the standard\n results are reproduced. As an example, we study discrete-symmetry\n breaking in a mean-field model for a commensurate charge-density wave.\n An additional benefit of the approach is that away from the critical\n temperature for the breaking of discrete symmetries large interactions\n can be avoided at all RG scales.