Related papers: Weakly non-planar dimers
We study the dimer $XXZ$ spin model on two-leg ladders with isotropic Heisenberg interactions on the rung and anisotropic $XXZ$ interactions along the rail in an external field. Combining both analytical and numerical methods, we set up the…
We apply the Grassmannian representation of the dimer model, an equivalent approach to Kasteleyn's solution to the close-packed dimer problem, to calculate the connection probabilities for the double-dimer model with wired/free/wired/free…
We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-like models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original…
Band flattening has been identified as key ingredient to correlation phenomena in Moir\'e materials and beyond. Here, we examine strongly repulsive fermions on a ladder -- a minimal platform for unconventional $d$-wave pairing -- and show…
The classical 1961 solution to the problem of determining the number of perfect matchings (or dimer coverings) of a rectangular grid graph -- due independently to Kasteleyn and to Temperley and Fisher -- consists of changing the sign of…
We present a fermion model that is, as we suggest, a natural 2D analogue of the Luttinger model. We derive this model as a partial continuum limit of a 2D spinless lattice fermion system with local interactions and away from half filling.…
We analyse the asymptotic symmetries of electromagnetism non-minimally coupled to scalar fields, with non-minimal couplings of the Fermi type that occur in extended supergravity models. Our study is carried out at spatial infinity where…
In a recent paper [ F. Wang and F. Y. Wu, Phys. Rev. E 75 (2007) 040105(R) ] we reported exact results on the enumeration of close-packed dimers on an infinite kagome lattice. We computed the per-dimer free energy using both the Pfaffian…
A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical…
We study a generalisation of the double-dimer model that encompasses several models of interest, including the monomer double-dimer model, spatial random permutations, the dimer model, and the spin $O(N)$ model, and which is also related to…
This note relates topics in statistical mechanics, graph theory and combinatorics, lattice quantum field theory, super quantum mechanics and string theory. We give a precise relation between the dimer model on a graph embedded on a torus…
The perturbation expansion for a general class of many-fermion systems with a non-nested, non-spherical Fermi surface is renormalized to all orders. In the limit as the infrared cutoff is removed, the counterterms converge to a finite limit…
This paper completes the comprehensive study of the dimer model on infinite minimal graphs with Fock's weights [arXiv:1503.00289] initiated in [arXiv:2007.14699]: the latter article dealt with the elliptic case, i.e., models whose…
This is a contribution to the number theory of the dimer problem. The number of dimer coverings (i.e., perfect matchings) of a square lattice graph is discussed modulo powers of 2.
Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common…
In the first part of this note, we observe that a non-Riemannian piece in the affine connection (a "dark connection") leads to an algebraically determined, conserved, symmetric 2-tensor in the Einstein field equations that is a natural dark…
In this thesis, I study a two-dimensional extended Hubbard model in the weak coupling limit. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons. However in the special case of a…
This paper provides a comprehensive study of the dimer model on infinite minimal graphs with Fock's elliptic weights [arXiv:1503.00289]. Specific instances of such models were studied in [arXiv:052711, arXiv:1612.09082, arXiv1801.00207]; we…
I discuss the 2-flavor Schwinger model with $\theta=0$ and small equal and opposite fermion masses (or $\theta=\pi$ with equal masses). The massless model has an unparticle sector with unbroken conformal symmetry. I argue that this special…
The notion of the integral over the anticommuting Grassmann variables is applied to analyze the fermionic structure of the 2D Ising model with quenched site dilution. In the $N$-replica scheme, the model is explicitly reformulated as a…