Snapshot Spectrum and Critical Phenomenon for Two-Dimensional Classical Spin Systems

Exact mapping between classical and topological orders in two-dimensional spin systems

Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with topological orders can be constructed from certain well-known models with classical orders characterized by symmetry breaking. Topology-dependent ground state ...

Semi-classical Analysis of Spin Systems near Critical Energies

Casimir Terms and Shape Instabilities for Two-Dimensional Critical Systems

We calculate the universal part of the free energy of certain finite two-dimensional regions at criticality by use of conformal field theory. Two geometries are considered: a section of a circle ("pie slice") of angle φ and a helical staircase of finite angular (and radial) extent. We derive some consequences for certain matrix elements of the transfer matrix and corner transfer matrix. We exam...

Critical thermodynamics of the two-dimensional +/-J Ising spin glass.

We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an "effective" gap of size 2J; in addition, an associated crossover length sca...

Critical level spacing distribution of two - dimensional disordered systems with spin - orbit coupling

The energy level statistics of 2D electrons with spin-orbit scattering are considered near the disorder induced metal-insulator transition. Using the Ando model, the nearest-level-spacing distribution is calculated numerically at the critical point. It is shown that the critical spacing distribution is size independent and has a Poisson-like decay at large spacings as distinct from the Gaussian...