Related papers: Some new exact critical-point amplitudes

We go beyond a systematic review of the semiclassical approaches for determining the scaling dimensions of fixed-charge operators in $U(1)$ and $O(N)$ models by introducing a general strategy apt at determining the relation between a given…

We present a critical analysis of Pade-based methods for the unitarization of low energy amplitudes. We show that the use of certain Pade Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we…

A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without…

We study the nonrelativistic limit of the quantum theory of a real scalar field with quartic self-interaction. The two body scattering amplitude is written in such way as to separate the contributions of high and low energy intermediary…

We consider the universality class of the two-dimensional Tricritical Ising Model. The scaling form of the free-energy naturally leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We…

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups $U(N)$, $O(N)$ and…

The field of scattering amplitudes plays a central role in elementary-particle physics. This includes various problems of broader interest for collider physics, gravitational physics, and fundamental principles underlying quantum field…

Threshold expansions of the $\pi\pi$ and $K\overline{K}$ spin 0 and isospin 0 scattering amplitudes are performed. Scattering lengths, effective ranges and so--called volume parameters are evaluated. Good agreement with the existing…

We solve the loop equations to all orders in $1/N^2$, for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for…

The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal…

Entropy accumulation near a quantum critical point was expected based on general scaling arguments, and has recently been explicitly observed. We explore this issue further in two canonical models for quantum criticality, with particular…

$\mathrm{O}(N)$ vector models in three dimensions, when defined in a geometry with a compact direction and tuned to criticality, exhibit long-range fluctuations which induce a Casimir effect. The strength of the resulting interaction is…

We describe the nonzero temperature (T), low frequency (\omega) dynamics of the order parameter near quantum critical points in two spatial dimensions (d), with a special focus on the regime \hbar\omega << k_B T. For the case of a…

Critical phenomena have been extensively investigated both theoretically and experimentally in many fields, such as condensed matter physics, biology, e.g., brain criticality, and cosmology. In particular, the behaviour of response…

We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a fermionic observable and compute its scaling limit by discrete…

We derive the complete set of partial wave unitarity bounds on the most general Axion-Like Particle (ALP) effective interactions up to dimension 8 in the limit of large center-of-mass energy. Exploiting a recently developed formalism based…

We consider the critical behaviour of long-range $O(n)$ models ($n \ge 0$) on ${\mathbb Z}^d$, with interaction that decays with distance $r$ as $r^{-(d+\alpha)}$, for $\alpha \in (0,2)$. For $n \ge 1$, we study the $n$-component…

For the case of the single-O($N$)-vector linear sigma models the critical behaviour following from any $A_k$ singularity in the action is worked out in the double scaling limit $N \rightarrow \infty$, $f_r \rightarrow f_r^c$, $2 \leq r \leq…

We analyze universal and nonuniversal finite-size effects of lattice systems in a $L^d$ geometry above the upper critical dimension d = 4 within the O(n) symmetric $\phi^4$ lattice theory. On the basis of exact results for $n \to\infty$ and…

In quantum theory, physical amplitudes are usually presented in the form of Feynman perturbation series in powers of coupling constant $\al .$ However, it is known that these amplitudes are not regular functions at $\alpha=0 .$ For QCD, we…