Mario Pernici

Wave equations for arbitrary spin from quantization of the extended supersymmetric spinning particle

Abstract We present the action for a relativistic particle with a gauged N-extended line supersymmetry and show that, upon quantization, it yields a relativistic wave equation for pure spin 1 2 N . A curved-space background is compatible with worldline supersymmetry only for N⩽2.

Yang-Lee edge singularities from extended activity expansions of the dimer density for bipartite lattices of dimensionality 2 d 7

We have extended, in most cases through 24th order, the series expansions of the dimer density in powers of the activity in the case of bipartite [(hyper)-simple-cubic and (hyper)-body-centered-cubic] lattices of dimensionalities 2 ≤ d ≤ 7. A numerical analysis of these data yields estimates of the exponents characterizing the Yang-Lee edge singularities for lattice ferromagnetic spin models as d varies between the lower and the upper critical dimensionalities. Our results are consistent with, but more extensive and sometimes more accurate than, those obtained from the existing dimer series or from the estimates of related exponents for lattice animals, branched polymers, and fluids. We mention also that it is possible to obtain estimates of the dimer constants from our series for the various lattices.

Higher order expansions for the entropy of a dimer or a monomer-dimer system on d-dimensional lattices

Recently, an expansion as a power series in 1/d has been presented for the specific entropy of a complete dimer covering of a d-dimensional hypercubic lattice. This paper extends from 3 to 10 the number of terms known in the series. Likewise, an expansion for the entropy, dependent on the dimer density p, of a monomer-dimer system, involving a sum ∑(k)a(k)(d)p(k), has been offered recently. We herein extend the number of known expansion coefficients from 6 to 20 for the hypercubic lattices of general dimensionality d and from 6 to 24 for the hypercubic lattices of dimensionalities d<5. We show that these extensions can lead to accurate numerical estimates of the p-dependent entropy for lattices with dimension d>2. The computations of this paper have led us to make the following marvelous conjecture: In the case of the hypercubic lattices, all the expansion coefficients a(k)(d) are positive. This paper results from a simple melding of two disparate research programs: one computing to high orders the Mayer series coefficients of a dimer gas and the other studying the development of entropy from these coefficients. An effort is made to make this paper self-contained by including a review of the earlier works.

Chiral invariance and lattice fermions with minimal doubling

Abstract A few years ago some attention has been given to a fermionic action on the lattice, with a Wilson-like term which is chirally invariant but breaks the hypercubic space-time lattice symmetry. This action describes two Dirac fields in the continuum limit, provided the coefficient λ of the Wilson-like term satisfies λ > 1 2 . In this letter it is shown that for 1 2 the theory is link-reflection positive. The propagator has the expected real energy poles. Modulo a phase shift on the fermions, the only relevant terms which can be added to the action respecting its symmetries have dimension 4.

Large order Reynolds expansions for the Navier–Stokes equations

Abstract We consider the incompressible homogeneous Navier–Stokes (NS) equations on a torus (typically, in dimension 3); we improve previous results of Morosi and Pizzocchero (2014) on the approximation of the solution via an expansion in powers of the Reynolds number. More precisely, we propose this approximation technique in the C ∞ setting of Morosi and Pizzocchero (2015) and present new applications, based on a Python program for the symbolic computation of the expansion. The a posteriori analysis of the approximants constructed in this way indicates, amongst else, global existence of the exact NS solution when the Reynolds number is below an explicitly computable critical value, depending on the initial datum; some examples are given.

The Blume–Capel model for spins S=1 and 3∕2 in dimensions d=2 and 3

Abstract Expansions through the 24th order at high-temperature and up to 11th order at low-temperature are derived for the main observables of the Blume–Capel model on bipartite lattices ( s q , s c and b c c ) in 2 d and 3 d with various values of the spin and in presence of a magnetic field. All expansion coefficients are computed exactly as functions of the crystal and magnetic fields. Several critical properties of the model are analyzed in the two most studied cases of spin S = 1 and S = 3 ∕ 2 .

A positivity property of the dimer entropy of graphs

The entropy of a monomer–dimer system on an infinite regular bipartite lattice can be written as a mean-field part plus a series expansion in the dimer density. In a previous paper it has been conjectured that all coefficients of this series are positive. Analogously on a connected regular graph with v vertices, the “entropy” of the graph lnN(i)/v, where N(i) is the number of ways of setting down i dimers on the graph, can be written as a part depending only on the number of the dimer configurations over the completed graph plus a Newton series in the dimer density on the graph. In this paper, we investigate for which connected regular graphs all the coefficients of the Newton series are positive (for short, these graphs will be called positive). In the class of connected regular bipartite graphs, up to v=20, the only non positive graphs have vertices of degree 3. From v=14 to v=30, the frequency of the positivity violations in the 3-regular graphs decreases with increasing v. In the case of connected 4-regular bipartite graphs, the first violations occur in two out of the 2806490 graphs with v=22. We conjecture that for each degree r the frequency of the violations, in the class of the r-regular bipartite graphs, goes to zero as v tends to infinity.

Hard-soft renormalization of the massless Wess-Zumino model

Abstract We show that in a Wilsonian renormalization scheme with zero-momentum subtraction point the massless Wess-Zumino model satisfies the non-renormalization theorem; the finite renormalization of the superpotential appearing in the usual non-zero momentum subtraction schemes is thus avoided. We give an exact expression of the beta and gamma functions in terms of the Wilsonian effective action; we prove the expected relation β =3 gγ . We compute the beta function at the first two loops, finding agreement with previous results.