Related papers: Shaping Lattice through irrelevant perturbation: I…
We investigate the presence of irrelevant operators in the 2d Ising model perturbed by a magnetic field, by studying the corrections induced by these operators in the spin-spin correlator of the model. To this end we perform a set of high…
We consider the Ising model on the Bethe lattice with aperiodic modulation of the couplings, which has been studied numerically in Phys. Rev. E 77, 041113 (2008). Here we present a relevance-irrelevance criterion and solve the critical…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
A fully anisotropic simple-cubic Ising lattice in the geometry of periodic cylinders $n\times n\times\infty$ is investigated by the transfer-matrix finite-size scaling method. In addition to the previously obtained critical amplitudes of…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic…
Experimental advances in condensed matter physics and material science have enabled ready access to atomic-resolution images, with resolution of modern tools often sufficient to extract minute details of symmetry-breaking distortions such…
By using conformal-field theory, we classify the possible irrelevant operators for the Ising model on the square and triangular lattices. We analyze the existing results for the free energy and its derivatives and for the correlation…
Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit…
The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interactions arise alongside bond-dependent couplings such as Kitaev ($K$) and $\Gamma$…
I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a…
We consider the critical behavior of two-dimensional layered Ising models where the exchange couplings between neighboring layers follow hierarchical sequences. The perturbation caused by the non-periodicity could be irrelevant, relevant or…
Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the…
We introduce and analyze a quantum spin/Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the…
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order…
We study the influence of an aperiodic extended surface perturbation on the surface critical behaviour of the two-dimensional Ising model in the extreme anisotropic limit. The perturbation decays as a power of the distance from the free…
A general approach for the description of spin systems on hierarchial lattices with coordination number $q$ as a dynamical variable is proposed. The ferromagnetic Ising model on the Bethe lattice was studied as a simple example…
We calculate the two-point correlation function and magnetic susceptibility in the anisotropic 2D Ising model on a lattice with one infinite and the other finite dimension, along which periodic boundary conditions are imposed. Using exact…