We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system. The method, originally developed by Suzuki [J. Phys. Soc. Jpn. 55, 4205 (1986)] for equilibrium systems, is based on the scaling properties of the singularity in the response functions determined through cluster mean-field calculations. We apply this method to the dissipative transverse-field Ising model and the dissipative $XYZ$ model in two dimensions obtaining convergent results already with small clusters.We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system. The method, originally developed by Suzuki [J. Phys. Soc. Jpn. 55, 4205 (1986)] for equilibrium systems, is based on the scaling properties of the singularity in the response functions determined through cluster mean-field calculations. We apply this method to the dissipative transverse-field Ising model and the dissipative $XYZ$ model in two dimensions obtaining convergent results already with small clusters.

arXiv:2103.07255Physical review. B./Physical review. BDec 1, 20217 citations

Recent theoretical estimates of the critical exponents

V. A. Rabinovich, Yu. E. Sheludyak

Journal of Engineering Physics and ThermophysicsNov 1, 19861 citation

Critical behavior of a 3D Ising-like system in the higher non-Gaussian approximation: Inclusion of the critical exponent of the correlation function

I. R. Yukhnovskii, Mykhailo P. Kozlovskii, Ihor V. Pylyuk

A microscopic description of the critical behavior of systems belonging to the universality class of the three-dimensional (3D) Ising model is developed within the collective variables (CV) approach. The higher non-Gaussian approximation (the sextic distribution for the modes of spin-moment density oscillations or the ρ6model) is used. A specific feature of the partition function calculation for an Ising-like system is the inclusion of the correction for the potential averaging. This correction leads to the modified recurrence relations (RR) for the ρ6model and a nonzero critical exponent of the correlation function η. The RR between the coefficients of the effective sextic distributions are written and analyzed. A technique for determining the small critical exponent η is elaborated in the higher non-Gaussian approximation. It is shown that the renormalized critical exponent of the correlation length has a tendency to a reduction in the case when the exponent η is taken into account.A microscopic description of the critical behavior of systems belonging to the universality class of the three-dimensional (3D) Ising model is developed within the collective variables (CV) approach. The higher non-Gaussian approximation (the sextic distribution for the modes of spin-moment density oscillations or the ρ6model) is used. A specific feature of the partition function calculation for an Ising-like system is the inclusion of the correction for the potential averaging. This correction leads to the modified recurrence relations (RR) for the ρ6model and a nonzero critical exponent of the correlation function η. The RR between the coefficients of the effective sextic distributions are written and analyzed. A technique for determining the small critical exponent η is elaborated in the higher non-Gaussian approximation. It is shown that the renormalized critical exponent of the correlation length has a tendency to a reduction in the case when the exponent η is taken into account.

International Journal of Modern Physics BJun 30, 20141 citation

Critical exponents from power spectra

K. B. Lauritsen, Hans C. Fogedby

Journal of Statistical PhysicsJul 1, 199325 citations

Scaling behavior in very small percolation lattices

J. B. Elliott, M. L. Gilkes, J. A. Hauger +7 more

We examine the average cluster distribution as a function of lattice probability for a very small $(L=6)$ lattice and determine the scaling function of three-dimensional percolation. The behavior of the second moment, calculated from the average cluster distribution of $L=6$ and $L=63$ lattices, is compared to power-law behavior predicted by the scaling function. We also examine the finite-size scaling of the critical point and the size of the largest cluster at the critical point. This analysis leads to estimates of the critical exponent $\ensuremath{\nu}$ and the ratio of critical exponents $\ensuremath{\beta}/\ensuremath{\nu}$.We examine the average cluster distribution as a function of lattice probability for a very small $(L=6)$ lattice and determine the scaling function of three-dimensional percolation. The behavior of the second moment, calculated from the average cluster distribution of $L=6$ and $L=63$ lattices, is compared to power-law behavior predicted by the scaling function. We also examine the finite-size scaling of the critical point and the size of the largest cluster at the critical point. This analysis leads to estimates of the critical exponent $\ensuremath{\nu}$ and the ratio of critical exponents $\ensuremath{\beta}/\ensuremath{\nu}$.

Physical Review CMar 1, 199727 citations

Scaling of fluctuations and critical exponents

M. Broidioi, M Van Canneyt

Journal of Statistical PhysicsJan 1, 19961 citation

XYZ

model in two dimensions obtaining convergent results already with small clusters.

We examine the average cluster distribution as a function of lattice probability for a very small

(L=6)

lattice and determine the scaling function of three-dimensional percolation. The behavior of the second moment, calculated from the average cluster distribution of

L=6

and

L=63

lattices, is compared to power-law behavior predicted by the scaling function. We also examine the finite-size scaling of the critical point and the size of the largest cluster at the critical point. This analysis leads to estimates of the critical exponent $\ensuremath{\nu}$ and the ratio of critical exponents $\ensuremath{\beta}/\ensuremath{\nu}$.