Scalarization-like mechanism through spacetime anisotropic scaling symmetry

Abstract The transport behavior of strongly anisotropic systems is significantly richer compared to isotropic ones. The most dramatic spatial anisotropy at a critical point occurs at a Lifshitz transition, found in systems with merging Dirac or Weyl point or near the superconductor-insulator quantum phase transition. Previous work found that in these systems a famous conjecture on the existence of a lower bound for the ratio of a shear viscosity to entropy is violated, and proposed a generalization of this bound for anisotropic systems near charge neutrality involving the electric conductivities. The present study uses scaling arguments and the gauge-gravity duality to confirm the previous analysis of universal bounds in anisotropic Dirac systems. We investigate the strongly-coupled phase of quantum Lifshitz systems in a gravitational Einstein-Maxwell-dilaton model with a linear massless scalar which breaks translations in the boundary dual field theory and sources the anisotropy. The holographic computation demonstrates that some elements of the viscosity tensor can be related to the ratio of the electric conductivities through a simple geometric ratio of elements of the bulk metric evaluated at the horizon, and thus obey a generalized bound, while others violate it. From the IR critical geometry, we express the charge diffusion constants in terms of the square butterfly velocities. The proportionality factor turns out to be direction-independent, linear in the inverse temperature, and related to the critical exponents which parametrize the anisotropic scaling of the dual field theory.

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Anisotropic Scaling of Random Fields with Long-Range Dependence

10.1142/12646 ◽

2023 ◽

Author(s):

Donatas Surgailis

Keyword(s):

Long Range ◽

Random Fields ◽

Long Range Dependence ◽

Anisotropic Scaling

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Highly Anisotropic Scaling Limits

Journal of Statistical Physics ◽

10.1007/s10955-015-1437-0 ◽

2015 ◽

Vol 162 (4) ◽

pp. 997-1030 ◽

Cited By ~ 1

Author(s):

M. Cassandro ◽

M. Colangeli ◽

E. Presutti

Keyword(s):

Scaling Limits ◽

Anisotropic Scaling

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Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields

SciPost Physics ◽

10.21468/scipostphys.8.3.032 ◽

2020 ◽

Vol 8 (3) ◽

Author(s):

Hendrik Hobrecht ◽

Fred Hucht

Keyword(s):

Ising Model ◽

Boundary Conditions ◽

Scaling Limit ◽

Finite Size ◽

Square Lattice ◽

Conformal Field ◽

Anisotropic Scaling ◽

Finite Lattices ◽

Antiferromagnetic Ising Model ◽

Boundary Fields

Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the finite-size scaling limit. Starting with the open cylinder, we independently apply boundary fields on both sides which can be either homogeneous or staggered, representing different combinations of boundary conditions. We confirm several predictions from scaling theory, conformal field theory and renormalisation group theory: we explicitly show that anisotropic couplings enter the scaling functions through a generalised aspect ratio, and demonstrate that open and staggered boundary conditions are asymptotically equal in the scaling regime. Furthermore, we examine the emergence of the surface tension due to one antiperiodic boundary in the system in the presence of symmetry breaking boundary fields, again for finite systems as well as in the scaling limit. Finally, we extend our results to the antiferromagnetic Ising model.

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