2019/11/27 by M. V. Kompaniets, A. Kudlis, A. I. Sokolov · 1 citation
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Combinatorics #Condensed matter physics #Critical exponent #Geometry #Loop (graph theory) #Mathematical physics #Mathematics #Order (exchange) #Phase (matter) #Phase diagram #Phase transition #Physics #Physics of Superconductivity and Magnetism #Plane (geometry) #Quantum chromodynamics #Quantum mechanics #Resummation #Series (stratigraphy) #Spin (aerodynamics) #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.nuclphysb.2019.114874
openalex publication_date 2019/11/27 · openalex created_date 2019/12/05 · arxiv created 2019/12/06 · arxiv updated 2020/01/08 · openalex updated_date 2026/08/05
The Landau-Wilson field theory with O(n)×O(m) symmetry which describes the critical thermodynamics of frustrated spin systems with noncollinear and noncoplanar ordering is analyzed in 4−ε dimensions within the minimal subtraction scheme in the six-loop approximation. The ε expansions for marginal dimensionalities of the order parameter nH(m,4−ε), n−(m,4−ε), n+(m,4−ε) separating different regimes of critical behavior are extended up to ε5 terms. Concrete series with coefficients in decimals are presented for m=2,…,6. The diagram of stability of nontrivial fixed points, including the chiral one, in (m,n) plane is constructed by means of summing up of corresponding ε expansions using various resummation techniques. Numerical estimates of the chiral critical exponents for several couples m,n are also found. Comparative analysis of our results with their counterparts obtained earlier within the lower-order approximations and by means of alternative approaches is performed. It is confirmed, in particular, that in physically interesting cases n=2,m=2 and n=2,m=3 phase transitions into chiral phases should be first-order.