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We study the domain of validity of a Schwinger-Dyson (SD) approach to non-equilibrium dynamics when there is broken symmetry. We perform exact numerical simulations of the one- and two-point functions of lambda phi^4 field theory in 1+1…
Spontaneous symmetry breaking occurs when the underlying laws of a physical system are symmetric, but the vacuum state chosen by the system is not. The (3+1)d $\phi^4$ theory is relatively simple compared to other more complex theories,…
We apply a new bosonization technique to relativistic field theories of fermions whose partition function is dominated by bosonic composites, and derive the effective action for these bosons. The derivation respects all symmetries,…
Matrix Models are the most effective way to describe strongly interacting systems with many degrees of freedom. They have proven successful in describing very different settings, from nuclei spectra to conduction in mesoscopic systems, from…
We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically…
The formation of scalar condensates and dynamical symmetry breaking in the U(n) four-fermion models (for n=2,3) with two coupling constants has been studied by the functional integration method. The bosonization procedures of the models…
A Hermitian $\Phi^4$ matrix model with a Kontsevich-type kinetic term is studied. It was recently discovered that the partition function of this matrix model satisfies the Schr\"odinger equation of the $N$-body harmonic oscillator, and that…
The aim of this paper is to determine the behavior of the specific heat of the 4-dimensional Ising model at the critical temperature, and via that determine if the Ising model and the $\phi^4$-model belong to the same universality class in…
We show that the spectrum of the three dimensional phi^4 theory in the broken symmetry phase contains non-perturbative states. We determine the spectrum using a new variational technique based on the introduction of operators corresponding…
The renormalized trajectory of massless $\phi^4$-theory on four dimensional Euclidean space-time is investigated as a renormalization group invariant curve in the center manifold of the trivial fixed point, tangent to the…
This paper studies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators. In a simpler…
We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q>4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting…
We study the O(N) $\phi^4$ model compactified on $M^{D-1}\otimes S^1$, which allows to impose twisted boundary conditions for the $S^1$-direction. The O(N) symmetry can be broken to $H$ explicitly by the boundary conditions and further…
Trained lattice samplers are usually judged by the ensembles they generate. Here we instead analyze the trained field-space function itself: a flow-matching velocity, a diffusion score, or a normalizing-flow action residual. We project…
We prove that any scaling limit of a critical reflection positive Ising or $\varphi^4$ model of effective dimension $d_{\text{eff}}$ at least four is Gaussian. This extends the recent breakthrough work of Aizenman and Duminil-Copin -- which…
Using the Griffiths-Simon construction of the $\varphi^4$ model and the lace expansion for the Ising model, we prove that, if the strength $\lambda\ge0$ of nonlinearity is sufficiently small for a large class of short-range models in…
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…
In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical…
A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry…
Semi-infinite $d$-dimensional systems with an $m$-axial bulk Lifshitz point are considered whose ($d-1$)-dimensional surface hyper-plane is oriented perpendicular to one of the $m$ modulation axes. An $n$-component $\phi^4$ field theory…