We present an accurate numerical determination of the crossover from classical to Ising-like critical behavior upon approach of the critical point in three-dimensional systems. The possibility of varying the Ginzburg number in our simulations allows us to cover the entire crossover region. We employ these results to scrutinize several semiphenomenological crossover scaling functions that are widely used for the analysis of experimental results. In addition, we present strong evidence that the exponent relations do not hold between effective exponents.We present an accurate numerical determination of the crossover from classical to Ising-like critical behavior upon approach of the critical point in three-dimensional systems. The possibility of varying the Ginzburg number in our simulations allows us to cover the entire crossover region. We employ these results to scrutinize several semiphenomenological crossover scaling functions that are widely used for the analysis of experimental results. In addition, we present strong evidence that the exponent relations do not hold between effective exponents.

arXiv:cond-mat/9807415Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsOct 1, 199857 citations

Critical behavior in trapped strongly interacting Fermi gases

Edward Taylor

We investigate the width of the Ginzburg critical region and experimental signatures of critical behavior in strongly interacting trapped Fermi gases close to unitarity, where the $s$ -wave scattering length diverges. Despite the fact that the width of the critical region is of the order unity, evidence of critical behavior in the bulk thermodynamics of trapped gases is strongly suppressed by their inhomogeneity. The specific heat of a harmonically confined gas, for instance, is linear in the reduced temperature $t=(T\ensuremath{-}{T}_{\text{c}})/{T}_{\text{c}}$ above ${T}_{\text{c}}$ . We also discuss the prospects of observing critical behavior in the local compressibility from measurements of the density profile.We investigate the width of the Ginzburg critical region and experimental signatures of critical behavior in strongly interacting trapped Fermi gases close to unitarity, where the $s$-wave scattering length diverges. Despite the fact that the width of the critical region is of the order unity, evidence of critical behavior in the bulk thermodynamics of trapped gases is strongly suppressed by their inhomogeneity. The specific heat of a harmonically confined gas, for instance, is linear in the reduced temperature $t=(T\ensuremath{-}{T}_{\text{c}})/{T}_{\text{c}}$ above ${T}_{\text{c}}$. We also discuss the prospects of observing critical behavior in the local compressibility from measurements of the density profile.

arXiv:0903.3030Physical Review AAug 19, 200921 citations

Testing Modern Theories of Critical Phenomena

Ole G. Mouritsen

Springer eBooksJan 1, 19840 citations

Crossover and Critical Behavior in the Layered XY Model

Roman Kracht, Andrea Trombettoni, Ilaria Maccari +1 more

Motivated by the interplay between 2D and 3D scaling signatures observed in unconventional layered superconductors, we present a systematic Monte Carlo study of the three-dimensional classical XY model with anisotropic in-plane $J_\parallel$ and inter-plane $J_\perp$ couplings. Our study includes very small values of the system anisotropy $Δ=J_\perp /J_\parallel$ not studied before, and focuses on characterizing the crossover from quasi-2D topological scaling to genuine 3D critical behavior. The numerical results for the critical temperature unambiguously reveal a logarithmic scaling with $Δ$ , directly related to the topological scaling in the 2D limit. Despite the 3D nature of the layered XY criticality, topological scaling signatures survive up to system sizes comparable to the crossover length $\ell_J$ , which diverges at small $Δ$ with a scaling behavior reminiscent of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This shows that genuine 3D symmetry-breaking behavior emerges only at exceedingly large system sizes when the anisotropy is very strong. Our results indicate that new experimental evidence is required to clarify the extent to which the critical signatures observed in layered strongly correlated materials are shaped by their pronounced anisotropy.Motivated by the interplay between 2D and 3D scaling signatures observed in unconventional layered superconductors, we present a systematic Monte Carlo study of the three-dimensional classical XY model with anisotropic in-plane $J_\parallel$ and inter-plane $J_\perp$ couplings. Our study includes very small values of the system anisotropy $Δ=J_\perp /J_\parallel$ not studied before, and focuses on characterizing the crossover from quasi-2D topological scaling to genuine 3D critical behavior. The numerical results for the critical temperature unambiguously reveal a logarithmic scaling with $Δ$, directly related to the topological scaling in the 2D limit. Despite the 3D nature of the layered XY criticality, topological scaling signatures survive up to system sizes comparable to the crossover length $\ell_J$, which diverges at small $Δ$ with a scaling behavior reminiscent of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This shows that genuine 3D symmetry-breaking behavior emerges only at exceedingly large system sizes when the anisotropy is very strong. Our results indicate that new experimental evidence is required to clarify the extent to which the critical signatures observed in layered strongly correlated materials are shaped by their pronounced anisotropy.

arXiv:2603.19351Mar 19, 20260 citations

Critical phenomena far from equilibrium

É. N. Rumanov

Uspekhi Fizicheskih NaukJan 1, 20139 citations

We investigate the width of the Ginzburg critical region and experimental signatures of critical behavior in strongly interacting trapped Fermi gases close to unitarity, where the

s

-wave scattering length diverges. Despite the fact that the width of the critical region is of the order unity, evidence of critical behavior in the bulk thermodynamics of trapped gases is strongly suppressed by their inhomogeneity. The specific heat of a harmonically confined gas, for instance, is linear in the reduced temperature $t=(T\ensuremath{-}{T}_{\text{c}})/{T}_{\text{c}}$ above

{T}_{\text{c}}

. We also discuss the prospects of observing critical behavior in the local compressibility from measurements of the density profile.

J_\parallel

and inter-plane

J_\perp

couplings. Our study includes very small values of the system anisotropy

Δ=J_\perp /J_\parallel

not studied before, and focuses on characterizing the crossover from quasi-2D topological scaling to genuine 3D critical behavior. The numerical results for the critical temperature unambiguously reveal a logarithmic scaling with

Δ

, directly related to the topological scaling in the 2D limit. Despite the 3D nature of the layered XY criticality, topological scaling signatures survive up to system sizes comparable to the crossover length

\ell_J

, which diverges at small

Δ

with a scaling behavior reminiscent of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This shows that genuine 3D symmetry-breaking behavior emerges only at exceedingly large system sizes when the anisotropy is very strong. Our results indicate that new experimental evidence is required to clarify the extent to which the critical signatures observed in layered strongly correlated materials are shaped by their pronounced anisotropy.