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A. Pelissetto

Publications and source records attributed to A. Pelissetto.

At least 19 recordsLinked to original sources
arXiv2015

Getting the Lorentz transformations without requiring an invariant speed

The structure of the Lorentz transformations follows purely from the absence of privileged inertial reference frames and the group structure (closure under composition) of the transformations---two assumptions that are simple and physically necessary. The existence of an invariant speed is \textit{not} a necessary assumption, and in fact is a consequence of the principle of relativity (though the finite value of this speed must, of course, be obtained from experiment). Von Ignatowsky derived this result in 1911, but it is still not widely known and is absent from most textbooks. Here we present a completely elementary proof of the result, suitable for use in an introductory course in special relativity.

gr-qc↗
arXiv2013

Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions

We study the universal critical behavior of two-dimensional (2D) lattice bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which separates the low-temperature superfluid phase from the high-temperature normal phase. For this purpose, we perform quantum Monte Carlo simulations of the hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the critical temperature by using a matching method that relates finite-size data for the BH model with corresponding data computed in the classical XY model. In this approach, the neglected scaling corrections decay as inverse powers of the lattice size L, and not as powers of 1/lnL, as in more standard approaches, making the estimate of the critical temperature much more reliable. Then, we consider the BH model in the presence of a trapping harmonic potential, and verify the universality of the trap-size dependence at the BKT critical point. This issue is relevant for experiments with quasi-2D trapped cold atoms.

cond-mat.quant-gas↗
arXiv2009

Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model

We consider the random-bond +- J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T*= 0.9527(1), p*=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, T=0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T T*. Our results for the critical exponents are consistent with the hyperscaling relation 2 beta/nu - eta = d - 2 = 0.

cond-mat.dis-nn↗
arXiv2008

Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models

We consider the two-dimensional randomly site diluted Ising model and the random-bond +-J Ising model (also called Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder. Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution.

cond-mat.dis-nn↗
arXiv2008

The critical behavior of 3D Ising glass models: universality and scaling corrections

We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin-glass models: the +-J Ising model for two values of the disorder parameter p, p=1/2 and p=0.7, and the bond-diluted +-J model for bond-occupation probability p_b = 0.45. A finite-size scaling analysis of the quartic cumulants at the critical point shows conclusively that these models belong to the same universality class and allows us to estimate the scaling-correction exponent omega related to the leading irrelevant operator, omega=1.0(1). We also determine the critical exponents nu and eta. Taking into account the scaling corrections, we obtain nu=2.53(8) and eta=-0.384(9).

cond-mat.dis-nn↗
arXiv2007

Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model

We consider the three-dimensional $\pm J$ model defined on a simple cubic lattice and study its behavior close to the multicritical Nishimori point where the paramagnetic-ferromagnetic, the paramagnetic-glassy, and the ferromagnetic-glassy transition lines meet in the T-p phase diagram (p characterizes the disorder distribution and gives the fraction of ferromagnetic bonds). For this purpose we perform Monte Carlo simulations on cubic lattices of size $L\le 32$ and a finite-size scaling analysis of the numerical results. The magnetic-glassy multicritical point is found at $p^*=0.76820(4)$, along the Nishimori line given by $2p-1={\rm Tanh}(J/T)$. We determine the renormalization-group dimensions of the operators that control the renormalization-group flow close to the multicritical point, $y_1 = 1.02(5)$, $y_2 = 0.61(2)$, and the susceptibility exponent $η= -0.114(3)$. The temperature and crossover exponents are $ν=1/y_2=1.64(5)$ and $ϕ=y_1/y_2 = 1.67(10)$, respectively. We also investigate the model-A dynamics, obtaining the dynamic critical exponent $z = 5.0(5)$.

cond-mat.dis-nn↗
arXiv2003

Critical equation of state of randomly dilute Ising systems

We determine the critical equation of state of three-dimensional randomly dilute Ising systems, i.e. of the random-exchange Ising universality class. We first consider the small-magnetization expansion of the Helmholtz free energy in the high-temperature phase. Then, we apply a systematic approximation scheme of the equation of state in the whole critical regime, that is based on polynomial parametric representations matching the small-magnetization of the Helmholtz free energy and satisfying a global stationarity condition. These results allow us to estimate several universal amplitude ratios, such as the ratio A^+/A^- of the specific-heat amplitudes. Our best estimate A^+/A^-=1.6(3) is in good agreement with experimental results on dilute uniaxial antiferromagnets.

cond-mat.stat-mech↗
arXiv2003

The three-dimensional randomly dilute Ising model: Monte Carlo results

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining $ν= 0.683(3)$, $η= 0.035(2)$, $β= 0.3535(17)$, and $α= -0.049(9)$, in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio $R^+_ξ$ that expresses the universality of the free-energy density per correlation volume. We find $R^+_ξ= 0.2885(15)$.

cond-mat.stat-mech↗
arXiv2003

Dynamic structure factor of the Ising model with purely relaxational dynamics

We compute the dynamic structure factor for the Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the $ε$ expansion, at two loops in the high-temperature phase and at one loop in the temperature magnetic-field plane, and a Monte Carlo simulation in the high-temperature phase. We find that the dynamic structure factor is very well approximated by its mean-field Gaussian form up to moderately large values of the frequency $ω$ and momentum $k$. In the region we can investigate, $kξ\lesssim 5$, $ωτ\lesssim 10$, where $ξ$ is the correlation length and $τ$ the zero-momentum autocorrelation time, deviations are at most of a few percent.

cond-mat.stat-mech↗
arXiv2002

Critical behavior of vector models with cubic symmetry

We report on some results concerning the effects of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. The analysis of the six-loop three-dimensional series provides an accurate description of the renormalization-group flow.

cond-mat.stat-mech↗
arXiv2002

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.

cond-mat.stat-mech↗
arXiv2001

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.

cond-mat.stat-mech↗
arXiv2000

The critical equation of state of the 2D Ising model

We compute the 2n-point coupling constants in the high-temperature phase of the 2d Ising model by using transfer-matrix techniques. This provides the first few terms of the expansion of the effective potential (Helmholtz free energy) and of the equation of state in terms of the renormalized magnetization. By means of a suitable parametric representation, we determine an analytic extension of these expansions, providing the equation of state in the whole critical region in the t,h plane.

cond-mat.stat-mech↗
arXiv2000

Critical exponents and equation of state of three-dimensional spin models

Three-dimensional spin models of the Ising and XY universality classes are studied by a combination of high-temperature expansions and Monte Carlo simulations. Critical exponents are determined to very high precision. Scaling amplitude ratios are computed via the critical equation of state. Our results are compared with other theoretical computations and with experiments, with special emphasis on the lambda transition of 4He.

hep-lat↗
arXiv2000

Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model

We discuss the analytic properties of the Callan-Symanzik beta-function beta(g) associated with the zero-momentum four-point coupling g in the two-dimensional phi^4 model with O(N) symmetry. Using renormalization-group arguments, we derive the asymptotic behavior of beta(g) at the fixed point g^*. We argue that beta'(g) = beta'(g^*) + O(|g-g^*|^{1/7}) for N=1 and beta'(g) = beta'(g^*) + O(1/\log |g-g^*|) for N > 2. Our claim is supported by an explicit calculation in the Ising lattice model and by a 1/N calculation for the two-dimensional phi^4 theory. We discuss how these nonanalytic corrections may give rise to a slow convergence of the perturbative expansion in powers of g.

hep-th↗
arXiv2000

Randomly dilute spin models: a six-loop field-theoretic study

We consider the Ginzburg-Landau MN-model that describes M N-vector cubic models with O(M)-symmetric couplings. We compute the renormalization-group functions to six-loop order in d=3. We focus on the limit N -> 0 which describes the critical behaviour of an M-vector model in the presence of weak quenched disorder. We perform a detailed analysis of the perturbative series for the random Ising model (M=1). We obtain for the critical exponents: gamma = 1.330(17), nu = 0.678(10), eta = 0.030(3), alpha=-0.034(30), beta = 0.349(5), omega = 0.25(10). For M > 1 we show that the O(M) fixed point is stable, in agreement with general non-perturbative arguments, and that no random fixed point exists.

cond-mat.stat-mech↗