Physical review. B, Condensed matter

Nonuniversal and surface critical behavior near a defect plane

Ferenc Iglói

Published Sep 1, 1989• 3 citations

Abstract

The existence of nonuniversal, as well as surface (universal) critical behavior near a defect plane is demonstrated on a one-dimensional quantum lattice gas model, belonging to the two-dimensional Ising universality class. According to numerical results the weak defect region is attracted by a line of fixed points starting at the bulk critical point, while the strong defect region is controlled by a separate fixed point describing the surface transition of the model. This new kind of phase diagram is argued to be general for two-dimensional lattice gas models.

DOI: 10.1103/physrevb.40.5187

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Physical review. B, Condensed matter

Nonuniversal and surface critical behavior near a defect plane

Ferenc Iglói

Published Sep 1, 1989• 3 citations

Publisher

Abstract

DOI: 10.1103/physrevb.40.5187

Related papers

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The local critical behavior of the

d

-dimensional

n

-vector model near an internal $d\ensuremath{-}1$ dimensional plane of weakened interactions in the limit $n\ensuremath{\rightarrow}\ensuremath{\infty}$ changes qualitatively at

d=3

. For

d>3

the critical exponent ${\ensuremath{\eta}}_{\ensuremath{\parallel}}$, which characterizes the correlation of spins in the defect plane, is universal, i.e., is independent of the strength of the interactions in the defect plane. We argue that ${\ensuremath{\eta}}_{\ensuremath{\parallel}}$ is nonuniversal for

d=3

and calculate its dependence on the difference between the defect and bulk couplings to second order in perturbation theory. We show that the excess energy density at a distance

z

from the defect plane decays at the critical point to the bulk value as ${z}^{\ensuremath{-}2}$ for $d\ensuremath{\ge}3$ and faster than ${z}^{\ensuremath{-}2}$ for

d<3

. Near the free surface of a semi-infinite system one finds a ${z}^{\ensuremath{-}2}$ dependence for

d>3

as well as for $d\ensuremath{\ge}3$.

{y}_{{t}_{1}}=0.718(2)

and

{y}_{{h}_{1}}=1.6465(6)

for the surface renormalization group exponents of the special transition. These results are compared with previous ones obtained by using field-theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore, we study the behavior of the surface transition near the special point, and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.

Criticality on Rényi Defects at (2+1)

D

O(3) Quantum Critical Points

D

quantum spin models realizing quantum phase transitions described by the O(3) Wilson-Fisher universality class, using large-scale quantum Monte Carlo simulations. We present numerical evidence that, for a fixed Rényi index

n

, there exist multiple Rényi defect universality classes, with distinct critical exponents for the O(3) order parameter on the defect. These universality classes are realized by choosing microscopically different entanglement cuts in lattice models, which we classify as ordinary, special and extraordinary according to their relation to surface criticality. For the extraordinary entanglement cut, we further find evidence for a phase transition on the defect as a function of the Rényi index. Our results highlight the key role of defect universality classes in determining the universal scaling of Rényi entropy, and provide a framework for understanding the previously observed dependence of Rényi entropy scaling on microscopic lattice details.