1,721,089 research outputs found
Spanning forests on random planar lattices
No full textThe generating function for spanning forests on a lattice is related to the q-state Potts model in a certain q
to 0 limit, and extends the analogous notion for spanning trees, or dense self-avoiding branched polymers. Recent works have found a combinatorial perturbative equivalence also with the (quadratic action) O(n) model
in the limit n to -1, the expansion parameter t counting the number of components of the forest.
We give a random-matrix formulation of this model on the ensemble of degree-k random planar lattices. For k=3, a correspondence is found with the Kostov solution of the loop-gas problem, which arise as
a reformulation of the (logarithmic action) O(n) model, at n=-2.
Then, we show how to perform an expansion around the t=0 theory. In
the thermodynamic limit, at any order in we have a finite sum of
finite-dimensional Cauchy integrals. The leading contribution comes from a
peculiar class of terms, for which a resummation can be performed
exactly
Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities II. Grassmann and quantum oscillator algebra representation
No full textWe prove that, for X, Y, A and B matrices with entries in a non-commutative ring such that [Xij,Ykl]=−AilBkj, satisfying suitable commutation relations (in particular, X is a Manin matrix), the following identity holds: coldetXcoldetY=. Furthermore, if also Y is a Manin matrix, coldetXcoldetY=∫D(ψ,ψ†)exp[∑k≥01k+1(ψ†Aψ)k(ψ†XBkYψ)]. Notations: , are respectively the bra and the ket of the ground state, a† and a the creation and annihilation operators of a quantum harmonic oscillator, while ψ†i and ψi are Grassmann variables in a Berezin integral. These results should be seen as a generalization of the classical Cauchy-Binet formula, in which A and B are null matrices, and of the non-commutative generalization, the Capelli identity, in which A and B are identity matrices and [Xij,Xkl]=[Yij,Ykl]=0
Absence of sign problem in the (saddle point approximation of the) nilpotency expansion of QCD at finite chemical potential
No full textWe have developed a method to derive the (approximate) quark contribution to the fermion free energy of QCD on a lattice, at finite temperature and chemical potential, with Kogut-Susskind fermions in the flavor basis.
We show here the expression at zero temperature. This result has been obtained at the lowest order of the nilpotency expansion. At this order the well known ``sign problem" does not arise and the quark contribution to the action can be used as a statistical weight in the Monte Carlo simulations
Quadratic Stochastic Euclidean Bipartite Matching Problem
Full text linkWe propose a new approach for the study of the quadratic stochastic Euclidean
bipartite matching problem between two sets of points each, . The
points are supposed independently randomly generated on a domain
with a given distribution on
. In particular, we derive a general expression for the correlation
function and for the average optimal cost of the optimal matching. A previous
ansatz for the matching problem on the flat hypertorus is obtained as
particular case
LATTICE PERTURBATION-THEORY FOR O(N)-SYMMETRICAL SIGMA-MODELS WITH GENERAL NEAREST-NEIGHBOR ACTION .1. CONVENTIONAL PERTURBATION-THEORY
No full textWe compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop beta-function. These results are used to compute the first analytic corrections to various long-distance quantities as the correlation length and the general spin-n susceptibility. It is found that these corrections are extremely large for RP(N-1) models (especially for small values of N), so that asymptotic scaling can be observed in these models only at very large values of beta. We also give the first three terms in the asymptotic expansion of the vector and tensor energies
4-LOOP PERTURBATIVE EXPANSION FOR THE LATTICE N-VECTOR MODEL
No full textWe compute the four-loop contributions to the beta-function and the anomalous dimension of the field for the O(N)-invariant N-vector model. These results are used to compute the second analytic corrections to the correlation length and the general spin-n susceptibility
Exact integration for height probabilities in the abelian sandpile model
No full textThe height probabilities for the recurrent configurations in the Abelian Sandpile model on the square lattice have analytic expressions, in terms of multidimensional quadratures. At first, these quantities were evaluated numerically with high accuracy and conjectured to be certain cubic rational- coefficient polynomials in 1/π. Later their values were determined by different methods.
We revert to the direct derivation of these probabilities, by computing analytically the corresponding integrals. Once again, we confirm the predictions on the probabilities, and thus, as a corollary, the conjecture on the average height, ⟨ρ⟩ = 17/8
One-dimensional Euclidean matching problem : exact solutions, correlation functions, and universality
Full text linkWe discuss the equivalence relation between the Euclidean bipartite matching problem on the line and on the circumference and the Brownian bridge process on the same domains. The equivalence allows us to compute the correlation function and the optimal cost of the original combinatorial problem in the thermodynamic limit; moreover, we solve also the minimax problem on the line and on the circumference. The properties of the average cost and correlation functions are discussed
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