Related papers: The fermionic observable in the Ising model and th…
We review some aspects of the fermionic interpretation of the two-dimensional Ising model. The use is made of the notion of the integral over the anticommuting Grassmann variables. For simple and more complicated 2D Ising lattices, the…
In this paper, we first rework B. Kaufman's 1949 paper, "Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis", by using representation theory. Our approach leads to a simpler and more direct way of deriving the spectrum…
This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here, we introduce spaces of…
We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (second-order) phase transition in the sense that there is a unique Gibbs measure at the critical temperature. The proof of this…
We address the quantum-critical behavior of a two-dimensional itinerant ferromagnetic systems described by a spin-fermion model in which fermions interact with close to critical bosonic modes. We consider Heisenberg ferromagnets, Ising…
We continue the study of non-commutative operator graphs generated by resolutions of identity covariant with respect to unitary actions of the circle group and the Heisenber-Weyl group as well. It is shown that the graphs generated by the…
Quadratic band touching in fermionic systems defines a universality class distinct from that of linear Dirac points, yet its characterization as a quantum critical point remains incomplete. In this work, I show that a $(d+1)$-dimensional…
Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In…
In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of…
The lace expansion has been a powerful tool for investigating mean-field behavior for various stochastic-geometrical models, such as self-avoiding walk and percolation, above their respective upper-critical dimension. In this paper, we…
In this paper we construct a non-commutative geometry over a configuration space of gauge connections and show that it gives rise to a candidate for an interacting, non-perturbative quantum gauge theory coupled to a fermionic field on a…
We study the $\pm J$ three-dimensional Ising model with a longitudinal anisotropic bond randomness on the simple cubic lattice. The random exchange interaction is applied only in the $z$ direction, whereas in the other two directions, $xy$…
We derive a formalism to express the spin algebra $\mathfrak{su}(2)$ in a spin $s$ representation in terms of the algebra of $L$ fermionic operators that obey the Canonical Anti-commutation Relations. We also give the reverse direction of…
These classical inequalities allow one to estimate the number of negative eigenvalues and the sums $S_{\gamma}=\sum |\lambda_i|^{\gamma}$ for a wide class of Schr\"{o}dinger operators. We provide a detailed proof of these inequalities for…
This paper gives a construction of certain asymptotic observables (Araki-Haag detectors) in ground state representations of gapped quantum spin systems. The construction is based on general assumptions which are satisfied e.g. in the Ising…
We study the critical and off-critical (Griffiths-McCoy) regions of the random transverse-field Ising spin chain by analytical and numerical methods and by phenomenological scaling considerations. Here we extend previous investigations to…
The Kac-Moody correction factor, first studied by Macdonald in the affine case, corrects the failure of an identity found by Macdonald in finite-dimensional root systems in 1972. Subsequntly this factor appeared in several formulas in the…
This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the…
A theorem of Kontsevich relates the homology of certain infinite dimensional Lie algebras to graph homology. We formulate this theorem using the language of reversible operads and mated species. All ideas are explained using a pictorial…
The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a…