Coupling to anisotropic elastic media: Magnetic and liquid-crystal phase transitions

Abstract

A generalization of the Larkin-Pikin-Sak model in which an n-component order parameter is coupled to a general anisotropic elastic continuum is studied using the c expansion. It is found that the fixed-point structure is the same as the isotropic model but that all fixed points are unstable with respect to anisotropic perturbations, independent of external boundary conditions. The compressible smectic-A to smectic-C liquidcrystal transition is also studied. It is found to be unaffected by elastic degrees of freedom and is, therefore, expected to have helium exponents, as previously predicted by de Gennes.

Critical behavior of the supersolid transition in Bose-Hubbard models

“…where the coefficientsũ = u + 12(v/c) 2 m 2 c 2 σ 2 /ρ s , κ = (v/c) 2 , and g = 2(v/c) 2 mcσ/ √ρ s . Closely related models have been studied in the context of the influence of elastic degrees of freedom on the behavior of magnetic systems near a critical point [24][25][26]. Depending on the number n of spin components, anisotropy of the elastic constants and the symmetry of the coupling between the elastic deformations and the order parameter fields one finds different stability scenarios for the various fixed points of the renormalization group recursion relations.…”

Strongly coupled quantum criticality with a Fermi surface in two dimensions: Fractionalization of spin and charge collective modes

“…However, a simple one-loop analysis shows that this is not a stable procedure: 47 at order 5 2 we generate additional quartic terms which have a different , q dependence than that in Eq. ͑3.5͒, and new relevant terms are generated at each successive order.…”

Critical Behavior of a Noncritical Field: Destruction of Smectic Order at the SmecticA−CTricritical Point and Implications for de Vries Behavior

“…The variety of systems exhibiting critical behavior is incredibly rich: ferromagnets, antiferromagnets, superconductors, liquid crystals, superfluids, and disorder driven metal-insulator transitions, to name a few. In many of these systems, there is a coupling between the critical order parameter (e.g., magnetization) and a noncritical field (e.g., underlying lattice elasticity), and the interplay between the two is a topic of significant importance [1]. It is known that critical fluctuations can induce weak singularities in the noncritical field; see, e.g., Ref.…”

“…The C phase order parameter c is the projection ofn onto the layering plane. Following de Gennes's observation [5] that the AC transition should belong to the 3d XY universality class, further analyses were performed [1,6,7], all of which incorporated layer fluctuations. As shown in Fig.…”

“…The analyses [1,6,7] did not consider AC transitions that are near a tricritical point (where first and second order phase boundaries meet). Early work on tricritical points in magnetic systems [8] established that tricritical fluctuations are larger than those for nontricritical transitions.…”