Related papers: Reflection positivity and phase transitions in lat…
We review the discovery of reflection positivity. We also explain a new geometric approach and proof of the reflection positivity property.
We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous…
We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d-dimensional unit sphere and the interactions are proportional to the…
The Boltzmann distribution encodes our subjective knowledge of the configuration in a classical lattice model, given only its Hamiltonian. If we acquire further information about the configuration from measurement, our knowledge is updated…
Phase transition in the two-dimensional $q$-state Potts model with random ferromagnetic couplings in the large-q limit is conjectured to be described by the isotropic version of the infinite randomness fixed point of the random…
In this note we continue our investigations of the representation theoretic aspects of reflection positivity, also called Osterwalder--Schrader positivity. We explain how this concept relates to affine isometric actions on real Hilbert…
Reflectionless potentials (RPs) represent a class of potentials that offer total transmission in the context of one dimensional scattering. Optical realization of RPs in stratified medium can exhibit broadband omnidirectional antireflection…
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the possible spin values (or colors). The resulting energy landscape is thus significantly…
We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In…
We consider stochastic dynamics of lattice systems with finite local state space, possibly at low temperature, and possibly non-reversible. We assume the additional regularity properties on the dynamics: a) There is at least one stationary…
The effect of quenched impurities on systems which undergo first-order phase transitions is studied within the framework of the q-state Potts model. For large q a mapping to the random field Ising model is introduced which provides a simple…
We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application…
Reprocessing of X-ray pulsar radiation by the atmosphere of a companion in a binary system may result in reflected pulse radiation with a period of the pulses equal to the period of the pulsar under suitable conditions. In this paper the…
In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising Models on lattices, and Mean-Field type Ising Models…
The reflection of a normally incident wideband pulse by a half-space whose permittivity and permeability obey the one-resonance Lorentz model is calculated. The results are compared with those from frequency-domain reflection analysis. In…
Photoreflectance (PR) is a convenient characterization tool able to reveal optoelectronic properties of semiconductor materials and structures. It is a simple non-destructive and contactless technique which can be used in air at room…
A class of kinetically constrained models with reflection symmetry is proposed as an extension of the Fredrickson-Andersen model. It is proved that the proposed model on the square lattice exhibits a freezing transition at a non-trivial…
Parity-time (PT) symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the PT symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are…
Reflection positivity constitutes an integral prerequisite in the Osterwalder-Schrader reconstruction theorem which relates quantum field theories defined on Euclidean space to their Lorentzian signature counterparts. In this work we…
We summarize how to obtain rough bounds for one version of the emptiness formation probability in the 2d dimer model. The methods we use are the same as have been developed to obtain EFP bounds in the 1d XXZ model in a paper with Crawford,…