TY - JOUR

T1 - Six-loop ε expansion study of three-dimensional O(n)×O(m) spin models

AU - Kompaniets, M.V.

AU - Kudlis, A.

AU - Sokolov, A.I.

N1 - Publisher Copyright: © 2019 The Author(s)

PY - 2020/1

Y1 - 2020/1

N2 - 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.

AB - 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.

KW - 2ND-ORDER TRANSITION

KW - CRITICAL-BEHAVIOR

KW - DYSPROSIUM

KW - HEISENBERG-ANTIFERROMAGNET

KW - MAGNETIC-STRUCTURE

KW - NEUTRON-DIFFRACTION

KW - ORDER

KW - PHASE-TRANSITIONS

KW - RENORMALIZATION-GROUP APPROACH

KW - SYSTEMS

KW - Multi-loop calculations

KW - Chiral model

KW - Frustrated spin systems

KW - ε expansion

KW - Critical exponents

KW - Marginal dimensionalities

KW - Renormalization group

UR - http://www.scopus.com/inward/record.url?scp=85092196572&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0d249045-195e-3a94-bfb1-7c1c47df4dc8/

U2 - 10.1016/j.nuclphysb.2019.114874

DO - 10.1016/j.nuclphysb.2019.114874

M3 - Article

VL - 950

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

M1 - 114874

ER -