Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model

Abstract

We consider m two-dimensional semi-infinite planes of Ising spins joined together through surface spins and study the critical behaviour near to the junction. The m=0 limit of the model - according to the replica trick - corresponds to the semi-infinite Ising model in the presence of a random surface field (RSFI). Using conformal mapping, second-order perturbation expansion around the weakly- and strongly-coupled planes limits and differential renormalization group, we show that the surface critical behaviour of the RSFI model is described by Ising critical exponents with logarithmic corrections to scaling, while at multiple junctions (m>2) the transition is first order. There is a spontaneous junction magnetization at the bulk critical point.

Old paper, for archiving. 6 pages, 1 figure, IOP macro, epsf

References in corpus (1)

• Conformal invariance and linear defects in the two-dimensional Ising model

Cited by in corpus (16)

• Critical phenomena at perfect and non-perfect surfaces
• Shannon and Rényi mutual information in quantum critical spin chains
• From four- to two-channel Kondo effect in junctions of XY spin chains
• Mixed-order phase transition of the contact process near multiple junctions
• Critical Casimir forces in the presence of random surface fields
• Mixed-order transition in the antiferromagnetic quantum Ising chain in a field
• Logarithmic corrections in the two-dimensional Ising model in a random surface field
• Critical phenomena on k-booklets
• Reflection Scattering Matrix of the Ising Model in a Random Boundary Magnetic Field
• Star junctions and watermelons of pure or random quantum Ising chains : finite-size properties of the energy gap at criticality
• Fluctuation induced forces in critical films with disorder at their surfaces
• Scaling properties at the interface between different critical subsystems: The Ashkin-Teller model
• Critical behavior of models with infinite disorder at a star junction of chains
• Nonuniversal and anomalous critical behavior of the contact process near an extended defect
• Ising model in a boundary magnetic field with random discontinuities
• Quantum Potts chain in alternating field