相关论文: Lattice $\phi^4$ Field Theory on Riemann Manifolds…

Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element…

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the Quantum Finite Elements method to…

We define a 2-dimensional Ising model on a triangulated sphere, $\mathbb S^2$, designed to approach the exact conformal field theory (CFT) in the continuum limit. Surprisingly, the derivation leads to a set of geometric constraints that the…

The quantum extension of classical finite elements, referred to as quantum finite elements ({\bf QFE})~\cite{Brower:2018szu,Brower:2016vsl}, is applied to the radial quantization of 3d $\phi^4$ theory on a simplicial lattice for the…

We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of $\phi^4$ theory on 2D square lattice is complete in the sense that the partition…

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 demonstrate that the Ising model on a general triangular graph with 3 distinct couplings $K_1,K_2,K_3$ corresponds to an affine transformed conformal field theory (CFT). Full conformal invariance of the $c= 1/2$ minimal CFT is restored…

We review the recent construction \cite{brower2024isingmodelmathbbs2} of the 2d Ising model on a triangulated sphere $\mathbb{S}^2$. Surprisingly, this led to a precise map of the lattice couplings to the target geometry in order to reach…

Lattice radial quantization was proposed in a recent paper by Brower, Fleming and Neuberger[1] as a nonperturbative method especially suited to numerically solve Euclidean conformal field theories. The lessons learned from the lattice…

The completeness of some classical statistical mechanical (SM) models is a recent result that has been developed by quantum formalism for the partition functions. In this paper, we consider a 2D classical $\phi^4$ filed theory whose…

We investigate an integrable property and observables of 2 dimensional N=(4,4) topological field theory defined on a discrete lattice by using the "orbifolding" and "deconstruction" methods. We show that our lattice model possesses the…

The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that…

We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…

In this letter we explore the perspectives for canonical simulations in the worldline formulation of a lattice field theory. Using the charged $\phi^4$ field in two dimensions as an example we present the details of the canonical…

We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As a pilot study we apply this method to the 3d \lambda \phi^4 model. The regularisation consists of a fuzzy sphere with radius R for the two…

We use the complex $\phi^4$ field at finite density as a model system for developing further techniques based on worldline formulations of lattice field theories. More specifically we: 1) Discuss new variants of the worm algorithm for…

The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…

Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its…

We discuss scalar conformal field theories (CFTs) that can be realized in structural phase transitions. The Landau condition and Lifshitz condition are reviewed, which are necessary conditions for a structural phase transition to be second…

A lattice simulation in the broken phase of four-dimensional (lambda Phi^4) theory in the Ising limit suggests that, in the continuum limit, the scalar condensate rescales by a factor different from the conventional wavefunction…