Multicritical point relations in three dual pairs of hierarchical-lattice Ising spin glasses

  title={Multicritical point relations in three dual pairs of hierarchical-lattice Ising spin glasses},
  author={Michael Hinczewski and A. Nihat Berker},
  journal={Physical Review B},
The Ising spin glasses are investigated on three dual pairs of hierarchical lattices, using exact renormalization-group transformation of the quenched bond probability distribution. The goal is to investigate a recent conjecture that relates, on such pairs of dual lattices, the locations of the multicritical points, which occur on the Nishimori symmetry line. Toward this end we precisely determine the global phase diagrams for these six hierarchical spin glasses, using up to $2.5\ifmmode\times… 

Figures and Tables from this paper

Location and properties of the multicritical point in the Gaussian and ±J Ising spin glasses

We use transfer-matrix and finite-size scaling methods to investigate the location and properties of the multicritical point of two-dimensional Ising spin glasses on square, triangular, and honeycomb

Locations of multicritical points for spin glasses on regular lattices.

  • Masayuki Ohzeki
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
A systematic technique is proposed, by an improved technique, giving more precise locations of the multicritical points on the square, triangular, and hexagonal lattices by carefully examining the relationship between two partition functions related with each other by the duality.

Multicritical points for spin-glass models on hierarchical lattices.

An improved conjecture is proposed to give more precise predictions of the multicritical points than the conventional one, inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data.

Multicritical Points of Potts Spin Glasses on the Triangular Lattice(General)

We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points,

Multicritical Nishimori point in the phase diagram of the +/-J Ising model on a square lattice.

We investigate the critical behavior of the random-bond +/-J Ising model on a square lattice at the multicritical Nishimori point in the T-p phase diagram, where T is the temperature and p is the

Finite-connectivity spin-glass phase diagrams and low-density parity check codes.

  • G. MiglioriniD. Saad
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2006
The location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB) are studied, extending similar calculations that have been performed in the past for the Bethe spin-glass problem.

Reentrant and forward phase diagrams of the anisotropic three-dimensional Ising spin glass.

The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice and the boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin- glass phase, as temperature is lowered.

Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices.

  • Masayuki Ohzeki
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted and are expected to be slightly lower than the probability of the quantum Gilbert-Varshamov bound with a zero encoding rate.

Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems: Ising and Blume–Emery–Griffiths Models

Renormalization group based on the Migdal–Kadanoff bond removal approach is often considered a simple and valuable tool to understand the critical behavior of complicated statistical mechanical



Exact location of the multicritical point for finite-dimensional spin glasses: a conjecture

We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and

Ising spin-glass critical and multicritical fixed distributions from a renormalization-group calculation with quenched randomness

The Ising model with a quenched random distribution of ferromagnetic and antiferromagnetic interactions has been investigated by tracking the probability distribution of interactions under rescaling.

Symmetry, complexity and multicritical point of the two-dimensional spin glass

We analyse models of spin glasses on the two-dimensional square lattice by exploiting symmetry arguments. The replicated partition functions of the Ising and related spin glasses are shown to have

Location of the Ising spin-glass multicritical point on Nishimori's line.

We present arguments, based on local gauge invariance, that the multicritical point of Ising spin-glasses should be located on a particular line of the phase diagram known as Nishimori's line

Exactly soluble Ising models on hierarchical lattices

Certain approximate renormalization-group recursion relations are exact for Ising models on special hierarchical lattices, as noted by Berker and Ostlund. These lattice models provide numerous

Mapping between hierarchical lattices by renormalisation and duality

The renormalisation group scheme of Migdal (1976) and Kadanoff (1976) is applied to a ferromagnetic Potts model on two hierarchical lattices: in the two cases the renormalisation transformation is

Phase transitions of the Ashkin-Teller model including antiferromagnetic interactions on a type of diamond hierarchical lattice.

Using the real-space renormalization-group transformation, we study the phase transitions of the Ashkin-Teller model including the antiferromagnetic interactions on a type of diamond hierarchical


An Ising model including field randomness and $\ifmmode\pm\else\textpm\fi{}J$ bond randomness is studied by renormalization-group theory in spatial dimensions $d=2$ and 3. In $d=3,$ with field

Phase diagrams and crossover in spatially anisotropic d = 3 Ising, XY magnetic, and percolation systems: exact renormalization-group solutions of hierarchical models.

Hierarchical lattices that constitute spatially anisotropic systems are introduced and global phase diagrams are obtained for Ising and XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.