arXiv subjects

G. O. Heymans

Publications and source records attributed to G. O. Heymans.

10 recordsLinked to original sources

arXiv2026

Weak- and strong-disorder effects in the continuous random-field Ising model

We discuss the weak- and strong-disorder effects in the continuous random-field Ising model using the distributional zeta-function method. In the weak-disorder regime, the vacuum is located at the origin, whereas in the strong-disorder regime, the vacuum is shifted from the origin. By performing the quenched-disorder average at the level of the effective action, we derive the quadratic and interaction terms. In the weak-disorder limit, we show that the infrared structure of the two-point correlation functions yields a decomposition of the physical field into correlated components with distinct scaling dimensions. This mechanism exhibits the characteristic $1/p^4$ behavior, which shifts the upper critical dimension to $d_c^{+}=6$. The universal critical behavior of the RFIM near this dimension is governed by a minimal infrared effective action. In the strong-disorder regime, we obtain a diagonal quadratic action with a discrete spectrum of massive modes. The absence of massless modes implies that conventional criticality may be replaced by a symmetry-restoration transition. The resulting spectral representation of correlation functions converges rapidly and remains well controlled in the infrared limit.

cond-mat.dis-nn↗

arXiv2026

Zero Point Density Fluctuations and Electron Brownian Motion

The fluctuations in the phonon vacuum state can lead to zero point density fluctuations in a material, which in turn lead to local zero point fluctuations of the dielectric properties of the material. We argue that the density fluctuations lead to a fluctuating force on a test charge, such as an electron, located a short distance outside of the material. This force is due to fluctuating dipole moments inside the material, and produces Brownian motion of the electron. We calculate the mean squared velocity of the electron in both the normal and transverse direction relative to the boundary of the material. The result is nonzero in both directions, but larger in the normal case. We estimate the magnitude of this quantum Brownian motion and find that, in some cases, it can exceed the effects of both thermal motion and quantum momentum uncertainty. This suggests that the effect may be observable, and could constitute a source of quantum noise in nanoscale devices. It also potentially offers a means to remotely sense zero point density fluctuations in a material.

cond-mat.mes-hall↗

arXiv2024

The generalized second law in Euclidean Schwarzschild black hole

We discuss the Bekenstein generalized entropy of a Schwarzschild black hole, with the contribution of an external matter field affected by degrees of freedom near the event horizon. In the Euclidean section of the Schwarzschild manifold, we consider an Euclidean quantum effective model, a scalar theory in the presence of an additive disorder field. The average of the Gibbs free energy over the ensemble of possible configurations of the disorder is obtained by the distributional zeta-function method. In the series representation for the average free energy, the effective actions give rise to generalized Schrödinger operators on Riemannian manifolds. Finally, is presented the generalized entropy density with the contributions of the black hole geometric entropy and the external matter fields. The validity of the generalized second law using Euclidean functional methods is obtained.

gr-qc↗

arXiv2024

The Casimir-Lifshitz formula for rectangular dielectric waveguide

We analyze the Casimir-Lifshitz effect associated with the electromagnetic field in the presence of a rectangular waveguide consisting of two distinct dielectric materials in a $(3+1)$-dimensional spacetime. We employ the surface mode technique to derive a generalized Lifshitz formula for this specific geometry. Our formulation accounts for the unique dielectric properties of the materials composing the waveguide, leading to a precise calculation of the Casimir-Lifshitz energy. In the asymptotic limit, our results recover the classical expressions for perfect reflecting boundaries. This work extends the applicability of the Lifshitz formula to more complex systems and provides valuable insights into the influence of dielectric materials on the electromagnetic Casimir effect.

quant-ph↗

arXiv2024

Bounds in partition functions of the continuous random field Ising model

We investigate the critical properties of continuous random field Ising model (RFIM). Using the distributional zeta-function method, we obtain a series representation for the quenched free energy. It is possible to show that for each moment of the partition function, the multiplet of $k$-fields the Gaussian contribution has one field with the contribution of the disorder and $(k-1)$-fields with the usual propagator. Although the non-gaussian contribution is non-perturbative we are able to show that the model is confined between two $\mathbb{Z}_2\times\mathcal{O}(k-1)$-symmetric models. Using arguments of lower critical dimension alongside with monotone operators, we show that the phase of the continuous RFIM can be restricted by an $\mathbb{Z}_2 \times \mathcal{O}(k-1) \to \mathcal{O}(k-2)$ phase transition.

cond-mat.dis-nn↗

arXiv2024

Critical Casimir effect in a disordered $O(2)$-symmetric model

Critical Casimir effect appears when critical fluctuations of an order parameter interact with classical boundaries. We investigate this effect in the setting of a Landau-Ginzburg model with continuous symmetry in the presence of quenched disorder. The quenched free energy is written as an asymptotic series of moments of the models partition function. Our main result is that, in the presence of a strong disorder, Goldstone modes of the system contribute either with an attractive or with a repulsive force. This result was obtained using the distributional zeta-function method without relying on any particular ansatz in the functional space of the moments of the partition function.

cond-mat.soft↗

arXiv2023

The vacuum energy with non-ideal boundary conditions via an approximate functional equation

We discuss the vacuum energy of a quantized scalar field in the presence of classical surfaces, defining bounded domains $Ω\subset {\mathbb{R}}^{d}$, where the field satisfies ideal or non-ideal boundary conditions. For the electromagnetic case, this situation describes the conductivity correction to the zero-point energy. Using an analytic regularization procedure, we obtain the vacuum energy for a massless scalar field at zero temperature in the presence of a slab geometry $Ω=\mathbb R^{d-1}\times[0, L]$ with Dirichlet boundary conditions. To discuss the case of non-ideal boundary conditions, we employ an asymptotic expansion, based on an approximate functional equation for the Riemann zeta-function, where finite sums outside their original domain of convergence are defined. Finally, to obtain the Casimir energy for a massless scalar field in the presence of a rectangular box, with lengths $L_{1}$ and $L_{2}$, i.e., $Ω=[0,L_{1}]\times[0,L_{2}]$ with non-ideal boundary conditions, we employ an approximate functional equation of the Epstein zeta-function.

math-ph↗

arXiv2023

Analog Model for Euclidean Wormholes Effects

Using results of statistical field theory for systems with an anisotropic disorder, we present an analog model for Euclidean wormholes and topological fluctuation effects in a Riemannian space $\mathcal{M}^\mathrm{d}$. The contribution of wormholes and topological fluctuations to the Euclidean gravitational functional integral is modeled by quenched randomness defined in the $\mathbb{R}^{\mathrm{d}}$ manifold. We obtain a disorder-averaged free energy by taking the average over all the realizations of the random fields. In the scenario of topology fluctuation, there appears a superposition of infinite branes that contribute to the physical quantities. All topology fluctuations can be understood as two distinct kinds of Euclidean wormholes: wormholes confined to one brane, and wormholes connecting different branes.

hep-th↗

arXiv2022

Restoration of a Spontaneously Broken Symmetry in an Euclidean Quantum $λφ^{4}_{d+1}$ model with Quenched Disorder

We investigate the low temperature behavior of a system in a spontaneously broken symmetry phase described by an Euclidean quantum $λφ^{4}_{d+1}$ model with quenched disorder. Using a series representation for the averaged generating functional of connected correlation functions in terms of the moments of the partition function, we study the effects of the disorder linearly coupled to the scalar field. To deal with the strongly correlated disorder in imaginary time, we employthe equivalence between the model defined in a $d$-dimensional space with imaginary time with the statistical field theory model defined on a space ${\mathbb R}^{d}\times S^{1}$ with anisotropic quenched disorder. Next, using fractional derivatives and stochastic differential equations we obtain at tree-level the Fourier transform of the correlation functions of the disordered system. In one-loop approximation, we prove that there is a denumerable collection of moments of the partition function that can develop critical behavior. Below the critical temperature of the pure system, with the bulk in the ordered phase, there are a large number of critical temperatures that take each of these moments from an ordered to a disordered phase. We show the emergence of generic scale invariance in the system.

hep-th↗

arXiv2022

Disorder Effects in Dynamical Restoration of Spontaneously Broken Continuous Symmetry

We discuss the Euclidean quantum $O(N)$ model with $N=2$ in a continuous broken symmetry phase. We study the system at low temperatures in the presence of quenched disorder linearly coupled to the scalar field. Performing an average over the ensemble of all realizations of the disorder, we represent the average free energy in terms of a series of the moments of the partition function. In the one-loop approximation, we prove that there is a denumerable collection of moments that lead the system to develop critical behavior. Our results indicate that in an equilibrium system, the strongly correlation of the disorder in imaginary produces generic scale invariance in the massive modes.

hep-th↗