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G. Palma

Publications and source records attributed to G. Palma.

At least 19 recordsLinked to original sources
arXiv2019

General method to perform Microcanonical Monte Carlo Simulations

Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient relaxation algorithms required to minimize the energy, the relevant extensive thermodynamic variable appearing in the probability distribution, which drives the system after a thermalization process to equilibrium. Nevertheless, the nature does not know about statistical ensembles and therefore it is desirable and a theoretical challenge to show how to perform efficient numerical simulations in the microcanonical ensemble. In this article, we present a method based on the concepts of configurational temperature estimator \cite{Rugh,GDP} and on stochastic dynamics to do it. The method is independent of the Monte Carlo update strategy, and can be implemented for both local update or cluster algorithms. We illustrate the main features of the method by performing a numerical simulation of the planar interacting classical spin system, known as the two-dimensional XY-model.

cond-mat.stat-mech↗
arXiv2017

Bouncing solutions from generalized EoS

We present an exact analytical bouncing solution for a closed universe filled with only one exotic fluid with negative pressure, obeying a Generalized Equations of State (GEoS) of the form $P(ρ)=Aρ+Bρ^λ$, where $A$, $B$ and $λ$ are constants. In our solution $A=-1/3$ and $λ=1/2$ and $B<0$ is kept as a free parameter. For particular values of the initial conditions, we obtain that our solution obeys Null Energy Condition (NEC), which allows us to reinterpret the matter source as that of a real scalar field, $ϕ$, with a positive kinetic energy and a potential $V(ϕ)$. We compute numerically the scalar field as a function of time as well as its potential $V(ϕ)$, and find an analytical function for the potential that fits very accurately with the numerical results obtained. The shape of this potential can be well described by a Gaussian-type of function, and hence, there is no spontaneous symmetry minimum of $V(ϕ)$. We further show that the bouncing scenario is structurally stable under small variations of the parameter $A$, such that a family of bouncing solutions can be find numerically, in a small vicinity of the value $A=-1/3$.

gr-qc↗
arXiv2016

Ensemble-free configurational temperature for spin systems

An estimator for the dynamical temperature in an arbitrary ensemble is derived in the framework of Bayesian statistical mechanics and the maximum entropy principle. We test this estimator numerically by a simulation of the two-dimensional XY-model in the canonical ensemble. As this model is critical in the whole region of temperatures below the Berezinski-Kosterlitz-Thouless critical temperature $T_{BKT}$, we use a generalization of Wolff's uni-cluster algorithm. The numerical results allow us to confirm the robustness of the analytical expression for the microscopic estimator of the temperature. This microscopic estimator has also the advantage that it gives a direct measure of the thermalization process and can be used to compute absolute errors associated to statistical fluctuations. In consequence, this estimator allows for a direct, absolute and astringent test of the ergodicity of the underlying Markov process, which encodes the algorithm used in a numerical simulation.

cond-mat.stat-mech↗
arXiv2016

Finite-size corrections to scaling of the magnetization distribution in the $2d$ $XY$-model at zero temperature

The zero-temperature, classical $XY$-model on an $L \times L$ square-lattice is studied by exploring the distribution $Φ_L(y)$ of its centered and normalized magnetization $y$ in the large $L$ limit. An integral representation of the cumulant generating function, known from earlier works, is used for the numerical evaluation of $Φ_L(y)$, and the limit distribution $Φ_{L \rightarrow \infty} (y) = Φ_0(y)$ is obtained with high precision. The two leading finite-size corrections $Φ_L (y) -Φ_0 (y) \approx a_1(L)\, Φ_1(y) + a_2(L)\,Φ_2(y)$ are also extracted both from numerics and from analytic calculations. We find that the amplitude $a_1(L)$ scales as $\ln(L/L_0) /L^2$ and the shape correction function $Φ_1 (y)$ can be expressed through the low-order derivatives of the limit distribution, $Φ_1 (y) = [\,y\, Φ_0 (y) + Φ'_0 (y)\,]'$. The second finite-size correction has an amplitude $a_2(L)\propto 1/L^2$ and one finds that $a_2\,Φ_2(y) \ll a_1 \,Φ_1(y)$ already for small system size ($L> 10$). We illustrate the feasibility of observing the calculated finite-size corrections by performing simulations of the $XY$-model at low temperatures, including $T = 0$.

cond-mat.stat-mech↗
arXiv2015

Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions

Motivated by the numerical simulation of systems which display quantum phase transitions, we present a novel application of the meron-cluster algorithm to simulate the quantum antiferromagnetic Heisenberg model coupled to an external uniform magnetic field both in one and in two dimensions. In the infinite volume limit and at zero temperature we found numerical evidence that supports a quantum phase transition very close to the critical values $B_{c}=2$ and $B_{c}=4$ for the system in one and two dimensions, respectively. For the one dimensional system, we have compared the numerical data obtained with analytical predictions for the magnetization density as a function of the external field obtained by scaling-behaviour analysis and Bethe Ansatz techniques. Since there is no analytical solution for the two dimensional case, we have compared our results with the magnetization density obtained by scaling relations for small lattice sizes and with the approximated thermodynamical limit at zero temperature guessed by scaling relations. Moreover, we have compared the numerical data with other numerical simulations performed by using different algorithms in one and two dimensions, like the directed loop method. The numerical data obtained are in perfect agreement with all these previous results, which confirms that the meron-algorithm is reliable for quantum Monte Carlo simulations and applicable both in one and two dimensions. Finally, we have computed the integrated autocorrelation time to measure the efficiency of the meron algorithm in one dimension.

cond-mat.stat-mech↗
arXiv2011

Constraint Effective Potential of the Magnetization in the Quantum XY Model

Using an improved estimator in the loop-cluster algorithm, we investigate the constraint effective potential of the magnetization in the spin $\tfrac{1}{2}$ quantum XY model. The numerical results are in excellent agreement with the predictions of the corresponding low-energy effective field theory. After its low-energy parameters have been determined with better than permille precision, the effective theory makes accurate predictions for the constraint effective potential which are in excellent agreement with the Monte Carlo data. This shows that the effective theory indeed describes the physics in the low-energy regime quantitatively correctly.

cond-mat.str-el↗
arXiv2009

Analytical computation of the magnetization probability density function for the harmonic 2D XY model

The probability density function (PDF) of some global average quantity plays a fundamental role in critical and highly correlated systems. We explicitly compute this quantity as a function of the magnetization for the two dimensional XY model in its harmonic approximation. Numerical simulations and perturbative results have shown a Gumbel-like shape of the PDF, in spite of the fact that the average magnetization is not an extreme variable. Our analytical result allows to test both perturbative analytical expansions and also numerical computations performed previously. Perfect agreement is found for the first moments of the PDF. Also for large volume and in the high temperature limit the distribution becomes Gaussian, as it should be. In the low temperature regime its numerical evaluation is compatible with a Gumbel distribution.

hep-lat↗
arXiv2009

Cluster Algorithm Renormalization Group Study of Universal Fluctuations in the 2D Ising Model

In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the advantages of cluster algorithms. As an application we considered the 2D Ising model and studied wether scale invariance or universality are possible underlying mechanisms responsible for the approximate "universal fluctuations" close to a so-called bulk temperature $T^*(L)$. "Universal fluctuations" was first proposed in [1] and stated that the probability density function of a global quantity for very dissimilar systems, like a confined turbulent flow and a 2D magnetic system, properly normalized to the first two moments, becomes similar to the "universal distribution", originally obtained for the magnetization in the 2D XY model in the low temperature region. The results for the critical exponents and the renormalization group flow of the probability density function are very accurate and show no evidence to support that the approximate common shape of the PDF should be related to both scale invariance or universal behavior.

cond-mat.stat-mech↗
arXiv2008

Evolution of perturbed accelerating relativistic shock waves

We study the evolution of an accelerating hyperrelativistic shock under the presence of upstream inhomogeneities wrinkling the discontinuity surface. The investigation is conducted by means of numerical simulations using the PLUTO code for astrophysical fluid dynamics. The reliability and robustness of the code are demonstrated against well known results coming from the linear perturbation theory. We then follow the nonlinear evolution of two classes of perturbing upstream atmospheres and conclude that no lasting wrinkle can be preserved indefinitely by the flow. Finally we derive analytically a description of the geometrical effects of a turbulent upstream ambient on the discontinuity surface.

astro-ph↗
arXiv2006

The one dimensional Hydrogen atom revisited

The one dimensional Schroedinger hydrogen atom is an interesting mathematical and physical problem to study bound states, eigenfunctions and quantum degeneracy issues. This 1D physical system gave rise to some intriguing controversy over more than four decades. Presently, still no definite consensus seems to have been reached. We reanalyzed this apparently controversial problem, approaching it from a Fourier transform representation method combined with some fundamental (basic) ideas found in self-adjoint extensions of symmetric operators. In disagreement with some previous claims, we found that the complete Balmer energy spectrum is obtained together with an odd parity set of eigenfunctions. Closed form solutions in both coordinate and momentum spaces were obtained. No twofold degeneracy was observed as predicted by the degeneracy theorem in one dimension, though it does not necessarily have to hold for potentials with singularities. No ground state with infinite energy exists since the corresponding eigenfunction does not satisfy the Schroedinger equation at the origin.

quant-ph↗
arXiv2005

Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model

Generalized universality, as recently proposed, postulates a universal non-Gaussian form of the probability density function (PDF) of certain global observables for a wide class of highly correlated systems of finite volume N. Studying the 2D XY -model, we link its validity to renormalization group properties. It would be valid if there were a single dimension 0 operator, but the actual existence of several such operators leads to T-dependent corrections. The PDF is the Fourier transform of the partition function Z(q) of an auxiliary theory which differs by a dimension 0 perturbation with a very small imaginary coefficient iq/N from a theory which is asymptotically free in the infrared. We compute the PDF from a systematic loop expansion of ln Z(q).

cond-mat.stat-mech↗
arXiv2001

Resonance enhancement of particle production during reheating

We found a consistent equation of reheating after inflation, which shows that for small quantum fluctuations the frequencies of resonance are slighted different from the standard ones. Quantum interference is taken into account and we found that at large fluctuations the process mimics very well the usual parametric resonance but proceed in a different dynamical way. The analysis is made in a toy quantum mechanical model and we discuss further its extension to quantum field theory.

gr-qc↗
arXiv2000

Finite size scaling in the 2D XY-model and generalized universality

In recent works (BHP), a generalized universality has been proposed, linking phenomena as dissimilar as 2D magnetism and turbulence. To test these ideas, we performed a MC study of the 2D XY-model. We found that the shape of the probability distribution function for the magnetization M is non Gaussian and independent of the system size --in the range of the lattice sizes studied-- below the Kosterlitz-Thoules temperature. However, the shape of these distributions does depend on the temperature, contrarily to the BHP's claim. This behavior is successfully explained by using an extended finite-size scaling analysis and the existence of bounds for M.

cond-mat.stat-mech↗
arXiv1999

Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model

Polyakov's calculation of the effective action for the 2d nonlinear sigma-Model is generalized by purely analytic means to include contributions which are not UV-divergent and which depend on the choice of block spin. An analytic approximation to the background field which determines the classical perfect action is given, and approximations to the 1-loop correction are found. The results should be useful for numerical simulations.

hep-lat↗
arXiv1999

1-Loop improved lattice action for the nonlinear sigma-model

In this paper we show the Wilson effective action for the 2-dimensional O(N+1)-symmetric lattice nonlinear sigma-model computed in the 1-loop approximation for the nonlinear choice of blockspin $Φ(x)$, $Φ(x)= \Cavϕ(x)/{|\Cavϕ(x)|}$,where $\Cav$ is averaging of the fundamental field $ϕ(z)$ over a square $x$ of side $\tilde a$. The result for $S_{eff}$ is composed of the classical perfect action with a renormalized coupling constant $β_{eff}$, an augmented contribution from a Jacobian, and further genuine 1-loop correction terms. Our result extends Polyakov's calculation which had furnished those contributions to the effective action which are of order $\ln \tilde a /a$, where $a$ is the lattice spacing of the fundamental lattice. An analytic approximation for the background field which enters the classical perfect action will be presented elsewhere.

hep-lat↗
arXiv1999

Some Remarks on Oscillating Inflation

In a recent paper Damour and Mukhanov describe a scenario where inflation may continue during the oscillatory phase. This effect is possible because the scalar field spends a significant fraction of each period of oscillation on the upper part of the potential. Such additional period of inflation could push perturbations after the slow roll regime to observable scales. Although in this work we show that the small region of the Damour-Mukhanov parameter q gives the main contribution to oscillating inflation, it was not satisfactory understood until now. Furthermore, it gives an expression for the energy density spectrum of perturbations, which is well behaved in the whole physical range of q .

astro-ph↗
arXiv1996

Self-consistent Calculation of Real Space Renormalization Group Flows and Effective Potentials

We show how to compute real space renormalization group flows in lattice field theory by a self-consistent method. In each step, the integration over the fluctuation field (high frequency components of the field) is performed by a saddle point method. The saddle point depends on the block-spin. Higher powers of derivatives of the field are neglected in the actions, but no polynomial approximation in the field is made. The flow preserves a simple parameterization of the action. In this paper we treat scalar field theories as an example.

hep-lat↗