Related papers: Some new exact critical-point amplitudes
A $d$-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size $L$ and ``temporal size'' $1/T $ ($T$ - temperature of the system) is considered in the spherical approximation under periodic…
We study the $O(4)$-symmetric $ \Phi^4 $-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $\lambda$. A high precision Monte Carlo simulation is performed by…
The scaling form of the free--energy near a critical point allows for the definition of various universal ratios of thermodynamical amplitudes. Together with the critical exponents they characterize the universality classes and may be…
Motivated by the recent interest in the criticality of open quantum many-body systems, we study nonlinear sigma models with complexified couplings as a general framework for nonunitary field theory. Applying the perturbative…
We study the optical conductivity sigma(Omega) of an electron system near a quantum-critical point with finite-wavelength ordering. sigma(Omega) vanishes in clean Galilean-invariant systems, unless electrons are coupled to dynamical…
In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these…
We study two-to-two scattering amplitudes of a scalar particle of mass $m$. For simplicity, we assume the presence of $\mathbb{Z}_2$ symmetry and that the particle is $\mathbb{Z}_2$ odd. We consider two classes of amplitudes: the fully…
The $O(N)$ model with scalar quartic interactions at its ultraviolet fixed point, and the $O(N)$ model with scalar cubic interactions at its infra-red fixed point are conjectured to be equivalent. This has been checked by comparing various…
The large Nc expansion of N=2 supersymmetric Yang-Mills theory with gauge group SU(Nc) has recently been shown to break down at singularities on the moduli space. We conjecture that by taking Nc to infinity and approaching the singularities…
We show that two-dimensional sigma models are equivalent to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, the corresponding conformal field…
A d-dimensional finite quantum model system confined to a general hypercubical geometry with linear spatial size L and ``temporal size'' 1/T (T - temperature of the system) is considered in the spherical approximation under periodic…
We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0*t**mu, and for…
An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We…
The out-of-equilibrium dynamics of the O(N+1) nonlinear sigma model in 1+1 dimensions is investigated in the large N limit. Regarding the nonlinearity as the effect of a suitable large coupling limit of the O(N+1) \phi^4 model, we first of…
In a recent paper [Phys. Rev. E \textbf{92}, 012123 (2015)] a modified $d$-dimensional $\Phi^4$ model was investigated which differs from the standard one in that the $\Phi^4$ term was replaced by a nonlocal one with a potential…
We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an…
Thirty years ago, Stanley showed that an O(n) spin model on a lattice tends to a spherical model as $n\to\infty$. This means that at any temperature the corresponding free energies coincide. This fundamental result, providing the basis for…
Using the numerical results of the finite-size scaling study of the q-state Potts model by Bloete and Nightingale, we obtain conjectured expressions for the universal amplitude of the free energy density.
We propose formulas for the $1/N$ correction to the sphere free energy of theories with 4-fermion interactions, which are conformal for $d>2$. We also propose a formula for the scalar $O(N)$ model. Expanding these formulas in small…
We study the celestial description of the $O(N)$ sigma model in the large $N$ limit as introduced by Coleman, Jackiw and Politzer. Focusing on three dimensions, we analyze the implications of a UV complete, all-loop order 4-point amplitude…