Universality, frustration and conformal invariance in two-dimensional random Ising magnets

Abstract

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferro- and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents $\gamma /\nu$, $\alpha /\nu$ and $\nu$ to be obtained, whenever a second-order transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure--Ising exponents. Contrary to the unfrustrated case, subdominant terms do not fit a simple, logarithmic-enhancement form. Our analysis also suggests a vertical critical line at and below the Nishimori point. Approaching this point along either the temperature axis or the Nishimori line, one finds non-diverging specific heats. A percolation-like ratio $\gamma /\nu$ is found upon analysis of the uniform susceptibility at the Nishimori point. Our data are also consistent with frustration inducing a breakdown of the relationship between correlation-length amplitude and critical exponents, predicted by conformal invariance for pure systems.

arXiv commentRevTeX code for 10 pages, 9 eps figures, to appear in Physical Review B (September 1999)

References in corpus (13)

• Critical Behavior of Random Bond Potts Models
• Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study
• Criticality in the two-dimensional random-bond Ising model
• Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions
• Critical Behaviour of the Randomly Spin--Diluted 2-d Ising Model --- A Grand Ensemble Approach
• High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions
• Tests of Conformal Invariance in Randomness Induced Second-Order Phase Transitions
• On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet
• Correlation decay and conformal anomaly in the two-dimensional random-bond Ising ferromagnet
• Correlation functions in the two-dimensional random-bond Ising model
• Two dimensional Ising spin glasses with non-zero ordering temperatures
• Logarithmic corrections to gap scaling in random-bond Ising strips
• Crossovers in the Two Dimensional Ising Spin Glass with ferromagnetic next-nearest-neighbor interactions

Cited by in corpus (31)

• Random Network Models and Quantum Phase Transitions in Two Dimensions
• The two-dimensional random-bond Ising model, free fermions and the network model
• Nishimori point in the 2D +/- J random-bond Ising model
• Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry
• Duality and Multicritical Point of Two-Dimensional Spin Glasses
• Locations of multicritical points for spin glasses on regular lattices
• Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models
• Multicritical points for the spin glass models on hierarchical lattices
• Strong disorder fixed points in the two-dimensional random-bond Ising model
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice
• Multicritical point of Ising spin glasses on triangular and honeycomb lattices
• Symmetry, complexity and multicritical point of the two-dimensional spin glass
• Self-dual random-plaquette gauge model and the quantum toric code
• Exact location of the multicritical point for finite-dimensional spin glasses: A conjecture
• On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
• Renormalization Group on hierarchical lattices in finite dimensional disordered Ising and Blume-Emery-Griffiths Models
• An exact algorithm for spin correlation functions of the two dimensional +/-J Ising spin glass in the ground state
• Duality in finite-dimensional spin glasses
• Correlation--function distributions at the Nishimori point of two-dimensional Ising spin glasses
• Tensor network Monte Carlo simulations for the two-dimensional random-bond Ising model
• Properties of the multicritical point of +/- J Ising spin glasses on the square lattice
• Nonequilibrium critical dynamics of the two-dimensional $\pm J$ Ising model
• Critical exponents at the Nishimori point
• Entanglement Entropy of the Two-Dimensional +-J Ising Model on the Nishimori Line
• Energy fluctuations at the multicritical point in two-dimensional spin glasses
• Nishimori point in random-bond Ising and Potts models in 2D
• Revisiting Nishimori multicriticality through the lens of information measures
• Boundary Criticality at the Nishimori Multicritical Point