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Massimo Campostrini

Publications and source records attributed to Massimo Campostrini.

At least 37 records · Page 2Linked to original sources
arXiv2005

Critical behavior in a non-local interface model

The Raise and Peel model is a recently proposed one-dimensional statistical model describing a fluctuating interface. The evolution of the model follows from the competition between adsorption and desorption processes. The model is non-local due to the possible occurrence of avalanches. At a special ratio of the adsorption-desorption rates the model is integrable and many rigorous results are known. Off the critical point, the phase diagram and scaling properties are not known. In this paper, we search for indications of phase transition studying the gap in the spectrum of the non-hermitian generator of the stochastic interface evolution. We present results for the gap obtained from exact diagonalization and from Monte Carlo estimates derived from temporal correlations of various observables.

cond-mat.stat-mech↗
arXiv2005

Supersymmetric Yang-Mills quantum mechanics in various dimensions

Supersymmetric Yang-Mills quantum mechanics (SYMQM) results from the dimensional reduction of the Yang-Mills field theory in $D$ space-time dimensions to a single point in the $D-1$ dimensional space. It can be also viewed as the effective quantum mechanics of zero momentum modes of the original theory. These systems were first considered in 80's as simple models with supersymmetry. Independently, zero-volume field theories (especially pure Yang-Mills) were employed as the starting point of the small volume expansion, which is an important theoretical tool complementary to early lattice calculations. Later the models attracted a new wave of interest after the hypothesis of the equivalence, between the $D=10, SU(\infty)$ SYMQM and a M-theory of D0 branes. In this talk some new results obtained for the D=4 system with SU(2) gauge symmetry will be presented.

hep-lat↗
arXiv2005

Dynamical supersymmetry breaking and phase diagram of the lattice Wess-Zumino model

We study dynamical supersymmetry breaking and the transition point by non-perturbative lattice techniques in a class of two-dimensional N=1 Wess-Zumino model. The method is based on the calculation of rigorous lower bounds on the ground state energy density in the infinite-lattice limit. Such bounds are useful in the discussion of supersymmetry phase transition. The transition point is determined with this method and then compared with recent results based on large-scale Green Function Monte Carlo simulations with good agreement.

hep-lat↗
arXiv2004

Phase diagram of the lattice Wess-Zumino model from rigorous lower bounds on the energy

We study the lattice N=1 Wess-Zumino model in two dimensions and we construct a sequence $ρ^{(L)}$ of exact lower bounds on its ground state energy density $ρ$, converging to $ρ$ in the limit $L\to\infty$. The bounds $ρ^{(L)}$ can be computed numerically on a finite lattice with $L$ sites and can be exploited to discuss dynamical symmetry breaking. The transition point is determined and compared with recent results based on large-scale Green Function Monte Carlo simulations with good agreement.

hep-lat↗
arXiv2004

Supersymmetry breaking in two dimensions: the lattice N=1 Wess-Zumino model

We study dynamical supersymmetry breaking by non perturbative lattice techniques in a class of two-dimensional N=1 Wess-Zumino models. We work in the Hamiltonian formalism and analyze the phase diagram by analytical strong-coupling expansions and explicit numerical simulations with Green Function Monte Carlo methods.

hep-lat↗
arXiv2002

On the evaluation of the improvement parameter in the lattice Hamiltonian approach to critical phenomena

In lattice Hamiltonian systems with a quartic coupling $γ$, a critical value $γ^*$ may exist such that, when $γ=γ^*$, the leading irrelevant operator decouples from the Hamiltonian and the leading nonscaling contribution to renormalization-group invariant physical quantities (evaluated in the critical region) vanishes. The 1/N expansion technique is applied to the evaluation of $γ^*$ for the lattice Hamiltonian of vector spin models with O(N) symmetry. As a byproduct, systematic asymptotic expansions for the relevant lattice massive one-loop integrals are obtained.

cond-mat.stat-mech↗
arXiv2002

Exact Witten Index in D=2 supersymmetric Yang-Mills quantum mechanics

A new, recursive method of calculating matrix elements of polynomial hamiltonians is proposed. It is particularly suitable for the recent algebraic studies of the supersymmetric Yang-Mills quantum mechanics in any dimensions. For the D=2 system with the SU(2) gauge group, considered here, the technique gives exact, closed expressions for arbitrary matrix elements of the hamiltonian and of the supersymmetric charge, in the occupation number representation. Subsequent numerical diagonalization provides the spectrum and restricted Witten index of the system with very high precision (taking into account up to $10^5$ quanta). Independently, the exact value of the restricted Witten index is derived analytically for the first time.

hep-th↗
arXiv2002

A Hamiltonian lattice study of the two-dimensional Wess-Zumino model

We investigate a Hamiltonian lattice version of the two-dimensional Wess-Zumino model by Quantum Monte Carlo simulations. In order to study the pattern of supersymmetry breaking, we measure the ground state energy and the correlation length along a trajectory approaching the continuum limit. The algorithm is very effective in measuring the ground state energy, and adequate for the correlation length.

hep-lat↗
arXiv2002

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining $γ=1.2373(2)$, $ν=0.63012(16)$, $α=0.1096(5)$, $η=0.03639(15)$, $β=0.32653(10)$, $δ=4.7893(8)$. Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate $Δ=0.52(3)$ for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.

cond-mat.stat-mech↗
arXiv2001

Hamiltonian Monte Carlo simulation of the two-dimensional Wess-Zumino model

We study a Hamiltonian lattice version of the two-dimensional Wess-Zumino model. Preliminary results obtained by Quantum Monte Carlo with a many-parameter guiding wave function are presented. We analyze the pattern of supersymmetry breaking by measuring the ground state energy and a set of supersymmetric Ward identities. The algorithm is quite effective and allows very precise measurements.

hep-lat↗
arXiv2001

Adaptive Optimization of Wave Functions for Lattice Field Models

The accuracy of Green Function Monte Carlo (GFMC) simulations can be greatly improved by a clever choice of the approximate ground state wave function that controls configuration sampling. This trial wave function typically depends on many free parameters whose fixing is a non trivial task. Here, we discuss a general purpose adaptive algorithm for their non-linear optimization. As a non trivial application we test the method on the two dimensional Wess-Zumino model, a relativistically invariant supersymmetric field theory with interacting bosonic and fermionic degrees of freedom.

hep-lat↗
arXiv2000

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. 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 the specific-heat amplitude ratio.

cond-mat.stat-mech↗
arXiv2000

Linked-Cluster Expansion of the Ising Model

The linked-cluster expansion technique for the high-temperature expansion of spin model is reviewed. A new algorithm for the computation of three-point and higher Green's functions is presented. Series are computed for all components of two-point Green's functions for a generalized 3D Ising model, to 25th order on the bcc lattice and to 23rd order on the sc lattice. Series for zero-momentum four-, six-, and eight-point functions are computed to 21st, 19th, and 17th order respectively on the bcc lattice.

cond-mat.stat-mech↗
arXiv2000

The critical equation of state of three-dimensional XY systems

We address the problem of determining the critical equation of state of three-dimensional XY systems. For this purpose we first consider the small-field expansion of the effective potential (Helmholtz free energy) in the high-temperature phase. We compute the first few nontrivial zero-momentum n-point renormalized couplings, which parametrize such expansion, by analyzing the high-temperature expansion of an improved lattice Hamiltonian with suppressed leading scaling corrections. These results are then used to construct parametric representations of the critical equation of state which are valid in the whole critical regime, satisfy the correct analytic properties (Griffith's analyticity), and take into account the Goldstone singularities at the coexistence curve. A systematic approximation scheme is introduced, which is limited essentially by the number of known terms in the small-field expansion of the effective potential. From our approximate representations of the equation of state, we derive estimates of universal ratios of amplitudes. For the specific-heat amplitude ratio we obtain A^+/A^-=1.055(3), to be compared with the best experimental estimate A^+/A^-=1.054(1).

cond-mat.stat-mech↗
arXiv1999

Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems

High-temperature series are computed for a generalized $3d$ Ising model with arbitrary potential. Two specific ``improved'' potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are: $γ=1.2371(4)$, $ν=0.63002(23)$, $α=0.1099(7)$, $η=0.0364(4)$, $β=0.32648(18)$. By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented.

cond-mat.stat-mech↗
arXiv1999

High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion

We determine the critical exponents for the XY universality class in three dimensions, which is expected to describe the $λ$-transition in ${}^4$He. They are obtained from the analysis of high-temperature series computed for a two-component $λϕ^4$ model. The parameter $λ$ is fixed such that the leading corrections to scaling vanish. We obtain $ν= 0.67166(55)$, $γ= 1.3179(11)$, $α=-0.0150(17)$. These estimates improve previous theoretical determinations and agree with the more precise experimental results for liquid Helium.

cond-mat.stat-mech↗