CJT effective potential approach to analyze the nature of phase transition of thermal QED$$_3$$ at finite volume

Based on the Cornwall–Jackiw–Tomboulis effective potential and the truncated Dyson–Schwinger equations, the nature of phase transition of thermal QED$$_3$$ 3 at finite volume is investigated. We show that, with the rise of temperature, the system undergoes a second-order transition in the chiral limit, and remains exhibiting the second-order with small fermion mass, while it switches to a crossover when the fermion mass exceeds a critical value about $$m_{c}$$ m c , which diminishes with the increasing volume size and tends to zero in infinite volume.

Non-integrable Ising Models in Cylindrical Geometry: Grassmann Representation and Infinite Volume Limit

In this paper, meant as a companion to Antinucci et al. (Energy correlations of non-integrable Ising models: the scaling limit in the cylinder, 2020. arXiv: 1701.05356), we consider a class of non-integrable 2D Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green’s function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries.

The disk partition function in string theory

We investigate the disk partition function for the open string. This is a subtle problem because of the presence of a residual gauge group PSL(2, ℝ) on the worldsheet even after fixing the conformal gauge. It naively has infinite volume and leads to a vanishing answer. We use different methods that all demonstrate that PSL(2, ℝ) effectively behaves like a group with finite negative volume in the path integral, which leads to a simple prescription for the computation of the disk partition function. We apply our findings to give a simple rederivation of the D-brane tensions.

Isospin-1/2 Dπ scattering and the lightest $$ {D}_0^{\ast } $$ resonance from lattice QCD

Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to mπ ≈ 239 MeV. The spectrum of the elastic Dπ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic Dπ scattering. By analytically continuing a range of scattering amplitudes, a $$ {D}_0^{\ast } $$ D 0 ∗ resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , and $$ {D}_0^{\ast } $$ D 0 ∗ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $$ {D}_0^{\ast } $$ D 0 ∗ is consistently found well below that of the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , in contrast to the currently reported experimental result.

A finite box as a tool to distinguish free quarks from confinement at high temperatures

Above the pseudocritical temperature $$T_c$$ T c of chiral symmetry restoration a chiral spin symmetry (a symmetry of the color charge and of electric confinement) emerges in QCD. This implies that QCD is in a confining mode and there are no free quarks. At the same time correlators of operators constrained by a conserved current behave as if quarks were free. This explains observed fluctuations of conserved charges and the absence of the rho-like structures seen via dileptons. An independent evidence that one is in a confining mode is very welcome. Here we suggest a new tool how to distinguish free quarks from a confining mode. If we put the system into a finite box, then if the quarks are free one necessarily obtains a remarkable diffractive pattern in the propagator of a conserved current. This pattern is clearly seen in a lattice calculation in a finite box and it vanishes in the infinite volume limit as well as in the continuum. In contrast, the full QCD calculations in a finite box show the absence of the diffractive pattern implying that the quarks are confined.

On the three-particle analog of the Lellouch-Lüscher formula

Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

Infinite-Volume Limit of Stochastic s-d System with Single-Component Impurity and s-Electron Spins

A Hamiltonian [Formula: see text], with locally smeared Ising-type s-d exchange between s-electrons and magnetic impurities, in a dilute magnetic alloy, is investigated. The Feynman-Kac theorem, Laplace expansion and Bogolyubov inequality are applied to obtain a lower and upper bound (lb and ub) on the system’s free energy per conducting electron [Formula: see text]. The two bounds differ, in the infinite-volume limit by a term [Formula: see text], linear in impurity concentration: lb[Formula: see text], ub[Formula: see text], [Formula: see text] denoting the Hamiltonian of the approximating mean-field s-d system. [Formula: see text] represents randomly positioned impurities interacting with a mean field implemented by the gas of conduction s-electrons, the latter interacting with the field of barriers and wells (according to the s-electron’s spin orientation) localized at the impurity sites. The inequality [Formula: see text] demonstrates increasing accuracy of the mean-field [Formula: see text]-theory, with decreasing impurity concentration.

Uniform Lipschitz Functions on the Triangular Lattice Have Logarithmic Variations

Uniform integer-valued Lipschitz functions on a domain of size N of the triangular lattice are shown to have variations of order $$\sqrt{\log N}$$ log N . The level lines of such functions form a loop O(2) model on the edges of the hexagonal lattice with edge-weight one. An infinite-volume Gibbs measure for the loop O(2) model is constructed as a thermodynamic limit and is shown to be unique. It contains only finite loops and has properties indicative of scale-invariance: macroscopic loops appearing at every scale. The existence of the infinite-volume measure carries over to height functions pinned at the origin; the uniqueness of the Gibbs measure does not. The proof is based on a representation of the loop O(2) model via a pair of spin configurations that are shown to satisfy the FKG inequality. We prove RSW-type estimates for a certain connectivity notion in the aforementioned spin model.

Spread out random walks on homogeneous spaces

A measure on a locally compact group is said to be spread out if one of its convolution powers is not singular with respect to Haar measure. Using Markov chain theory, we conduct a detailed analysis of random walks on homogeneous spaces with spread out increment distribution. For finite volume spaces, we arrive at a complete picture of the asymptotics of the n-step distributions: they equidistribute towards Haar measure, often exponentially fast and locally uniformly in the starting position. In addition, many classical limit theorems are shown to hold. In the infinite volume case, we prove recurrence and a ratio limit theorem for symmetric spread out random walks on homogeneous spaces of at most quadratic growth. This settles one direction in a long-standing conjecture.

Momentum space CFT correlators for Hamiltonian truncation

We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding to a Hamiltonian density) carries zero spatial momentum, but otherwise allowing operators to have arbitrary spin. A direct application of our formulas is the computation of Hamiltonian matrix elements within the framework of conformal truncation, a recently proposed method for numerically studying strongly-coupled QFTs in real time and infinite volume. Our momentum space formulas take the form of finite sums over 2F1 hypergeometric functions, allowing for efficient numerical evaluation. As a concrete application, we work out matrix elements for 3d ϕ4-theory, thus providing the seed ingredients for future truncation studies.