Related papers: The Critical Ising Model on a M\"obius Strip
Given a finite rhombus tiling of a polygonal region in the plane, the associated critical $Z$-invariant Ising model is invariant under star-triangle transformations. We give a simple matrix formula describing spin correlations between…
We study the conformal boundary conditions of the dilute O(n) model in two dimensions. A pair of mutually dual solutions to the boundary Yang-Baxter equations are found. They describe anisotropic special transitions, and can be interpreted…
Muon spin relaxation is a powerful technique for probing static and dynamic local magnetic fields. The strong collision model, based on a Gaussian-Markovian process, is commonly used to account for dynamical effects. Yet, it remains limited…
Ising models with nearest-neighbor ferromagnetic random couplings on a square lattice with a (1,1) surface are studied, using Monte Carlo techniques and star-tiangle transformation method. In particular, the critical exponent of the surface…
Boundary critical phenomena are studied in the 3- State Potts model in 2 dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and…
Starting from an exact formal identity for the two-state transverse Ising model and using correlation inequalities rigorous upper bounds for the critical temperature and the critical transverse field are obtained which improve effective…
Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An…
In many applications of spin models, the fast estimation of their critical temperatures and other physical properties is of great importance. In this work, we present the analytical expressions estimating the critical properties of…
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi- infinite…
We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve…
We consider pattern formation in periodically forced binary systems. In particular we focus on systems in which the two species are differentially forced, one being accelerated with respect to the other. Using a continuum model consisting…
We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but closer examination of the mechanism reveals that it…
The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in…
Statistical mechanical models with local interactions in $d>1$ dimension can be regarded as $d=1$ dimensional models with regular long range interactions. In this paper we study the critical properties of Ising models having $V$ sites, each…
We investigate the zero-temperature quantum phase transition of the random bond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two…
We consider the surface critical behaviour of a semi-infinite two-dimensional layered Ising model, where the couplings perpendicular to the surface follow the aperiodic Rudin-Shapiro sequence. The model has unusual critical properties:…
We develop a fully microscopic, statistical mechanics approach to study phase transitions in Ising systems with competing interactions at different scales. Our aim is to consider orientational and positional order parameters in a unified…
Using the formalism of differential equations, we introduce a new method to continuously deform the $s$-embeddings associated with a family of Ising models as their coupling constants vary. This provides a geometric interpretation of the…
Recent years witnessed an extensive development of the theory of the critical point in two-dimensional statistical systems, which allowed to prove {\it existence} and {\it conformal invariance} of the {\it scaling limit} for two-dimensional…
We explore the ground state properties of a lattice of classical dipoles spanned on the surface of a M\"{o}bius strip. The dipole equilibrium configurations depend significantly on the geometrical parameters of the M\"{o}bius strip, as well…