2000/11/09 by Andrey Mudrov, A. I. Mudrov, Mudrov, A. I. +2
Computer Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Nonlinear Dynamics and Pattern Formation #Physics of Superconductivity and Magnetism #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat #hep-th
paper · pdf · doi:10.48550/arxiv.cond-mat/0011167
6 pages, LaTeX, no figures. Talk presented at XXIII-rd Intern. Coll. "Group Theoretical Methods in Physics (Group-23)" (31 July - 5 August, JINR, Dubna, Russia, 2000). To be published in the Coll. Proceedings, JINR RAS, Dubna, 2001; insignificant misprints corrected, references and acknowledgment added
openalex publication_date 2000/11/09 · arxiv created 2000/11/19 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
The critical behavior of an MN-component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in (4-2\ve)-dimensions. Using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced for generic M and N and resummed by the Borel transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases M=2 and N=2, N=3 shows that the model has a three-dimensionally stable fixed point different from the Bose one. The critical dimensionality is proved to be exactly two times smaller than its counterpart in the real cubic model: NcC =1/2 NcR. The numerical value NcC=1.447 ± 0.020 is obtained from resumming the known five-loop \ve-series for NcR. Since NcC < 2, the critical thermodynamics of the model relevant to the phase transitions in real substances should be governed by the complex cubic fixed point with a new set of critical exponents: \gm=1.404(25), ν=0.715(10), \et=0.0343(20) for N=2 and \gm=1.390(25), ν=0.702(10), \et=0.0345(15) for N=3.