相关论文: Interpolating between $a$ and $F$

There have been a lot of methods aimed at studying the limiting free energy per particle (LFEPP) for 3-dimensional (3D) Ising model in absence of an external magnetic field. These methods are elegant, but most of them are complicated and…

We consider the transverse field Ising model in $(2+1)$D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a…

In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…

A formula is proposed for continuing physical correlation functions to non-integer numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is…

We use a functional approach to evaluate the Casimir free energy for a self-interacting scalar field in $d+1$ dimensions, satisfying Dirichlet boundary conditions on two parallel planes. When the interaction is turned off, exact results for…

We consider a higher derivative scalar field theory in the presence of a boundary and a classically marginal interaction. We first investigate the free limit where the scalar obeys the square of the Klein-Gordon equation. In precisely $d=6$…

We introduce a regularized free energy $\mathcal{F}_{\text{AdS}}$ for massive quantum field theories (QFTs) on Anti-de Sitter space (AdS). We conjecture this quantity to be monotonic under the renormalization group (RG) flow induced by…

We study the partition function of odd-dimensional conformal field theories placed on spheres with a squashed metric. We establish that the round sphere provides a local extremum for the free energy which, in general, is not a global…

We consider the continuation of free and interacting scalar field theory to non-integer spacetime dimension d. We find that the correlation functions in these theories are necessarily incompatible with unitarity (or with reflection…

We continue our study of $\lambda$-deformed $\sigma$-models by setting up a $1/k$ perturbative expansion around the free field point for cosets, in particular for the $\lambda$-deformed $SU(2)/U(1)$ coset CFT. We construct an interacting…

Parisi-Sourlas (PS) supersymmetry is known to emerge in some models with random field type of disorder. When PS SUSY is present the $d$-dimensional theory allows for a $d-2$-dimensional description. In this paper we investigate the reversed…

Computing electron-defect (e-d) interactions from first principles has remained impractical due to computational cost. Here we develop an interpolation scheme based on maximally localized Wannier functions (WFs) to efficiently compute e-d…

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling…

The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S^3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this…

The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…

Using the dS/QFT correspondence in the context of inflation allows for the study of interesting, otherwise inaccessible physics. In particular, by studying inflation via its dual field theory at the boundary of the de Sitter space, it may…

Fixed points of scalar field theories with quartic interactions in $d=4-\varepsilon$ dimensions are considered in full generality. For such theories it is known that there exists a scalar function $A$ of the couplings through which the…

We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…

We investigate the thermal properties of $\mathcal{PT}$-symmetric scalar field theories with purely imaginary couplings. The free energy governs the asymptotic density of states, providing an effective measure of the number of degrees of…

In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge $n$ operator in the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$ can be computed semiclassically for arbitrary values of $\lambda n$,…