We present an analytic study of finite-size effects on critical diffusion above and below ${T}_{c}$ of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size relaxation time that governs the critical order-parameter relaxation towards a metastable equilibrium state below ${T}_{c}.$ Two universal dynamic amplitude ratios at ${T}_{c}$ are predicted and quantitative predictions of dynamic finite-size scaling functions are given that can be tested by Monte Carlo simulations.We present an analytic study of finite-size effects on critical diffusion above and below ${T}_{c}$ of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size relaxation time that governs the critical order-parameter relaxation towards a metastable equilibrium state below ${T}_{c}.$ Two universal dynamic amplitude ratios at ${T}_{c}$ are predicted and quantitative predictions of dynamic finite-size scaling functions are given that can be tested by Monte Carlo simulations.

arXiv:cond-mat/9802206Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsAug 1, 199821 citations

Role of finite-size effects in the critical behavior of itinerant fermions

Avraham Klein, Andrey V. Chubukov

We study the role of finite-size effects on critical behavior near a metallic $q=0$ critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent $z=3$ . We show that finite-size effects are particularly strong for $z=3$ criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within $z=3$ theory.We study the role of finite-size effects on critical behavior near a metallic $q=0$ critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent $z=3$. We show that finite-size effects are particularly strong for $z=3$ criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within $z=3$ theory.

arXiv:1701.07557Physical review. B./Physical review. BJul 27, 20173 citations

Finite Size Effects in Critical Phenomena.

Jia Liang Han

Jan 1, 19870 citations

Finite size scaling effects in dynamics

Yadin Y. Goldschmidt

Nuclear Physics BJan 1, 198738 citations

We present an analytic study of finite-size effects on critical diffusion above and below

{T}_{c}

of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size relaxation time that governs the critical order-parameter relaxation towards a metastable equilibrium state below

{T}_{c}.

Two universal dynamic amplitude ratios at

{T}_{c}

are predicted and quantitative predictions of dynamic finite-size scaling functions are given that can be tested by Monte Carlo simulations.

We study the role of finite-size effects on critical behavior near a metallic

q=0

critical point and compare the results with a recent extensive quantum Monte Carlo (QMC) study [Y. Schattner et al., Phys. Rev. X 6, 031028 (2016)]. This study found several features in both bosonic and fermionic responses, in disagreement with the expected critical behavior with a dynamical exponent

z=3

. We show that finite-size effects are particularly strong for

z=3

criticality and give rise to a behavior different from that of an infinite system, over a wide range of momenta and frequencies. We argue that by taking finite-size effects into account, the QMC results can be explained within

z=3

theory.