相关论文: Critical even unimodular lattices in the Gaussian …

We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of $2$-modular lattices -- such as the $16$-dimensional Barnes-Wall lattice -- and $3$-modular lattices -- such as the $12$-dimensional…

The highest possible minimal norm of a unimodular lattice is determined in dimensions n <= 33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8*10^20 in dimension 33).…

We compute the fixed point index of non-degenerate central configurations for the $n$-body problem in the euclidean space of dimension $d$, relating it to the Morse index of the gravitational potential function $\bar U$ induced on the…

All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in $\mathbb{Q}(\sqrt{-3})$ are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3.

We classify the unimodular Euclidean integral lattices of rank 29 by developing an elementary, yet very efficient, inductive method. As an application, we determine the isometry classes of even lattices of rank at most 28 and prime…

We derive a mass formula for n-dimensional unimodular lattices having any prescribed root system. We use Katsurada's formula for the Fourier coefficients of Siegel Eisenstein series to compute these masses for all root systems of even…

It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24] +2, unless n = 23 when the bound must be increased by 1. This result was previously known only for even unimodular lattices. Quebbemann had extended the…

Given a polarization of an even unimodular lattice and integer $k\ge 1$, we define a family of unimodular lattices $L(M,N,k)$. Of special interest are certain $L(M,N,3)$ of rank 72. Their minimum norms lie in $\{4, 6, 8\}$. Norms 4 and 6 do…

In this paper and in the forthcoming Part II we introduce a Morse complex for a class of functions f defined on an infinite dimensional Hilbert manifold M, possibly having critical points of infinite Morse index and coindex. The idea is to…

Critical properties of the compact three-dimensional U(1) lattice gauge theory are explored at finite temperatures. The critical point of the deconfinement phase transition, critical indices and the string tension are studied numerically on…

In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar…

Based on universal arguments it is believed that there is a critical point (E) in QCD on the temperature (T) versus chemical potential (\mu) plane, which is of extreme importance for heavy-ion experiments. Using finite size scaling and a…

We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors.

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model…

For lengths up to 47 except 37, we determine the largest minimum Euclidean weight among all Type I Z4-codes of that length. We also give the first example of an optimal odd unimodular lattice in dimension 41 explicitly, which is constructed…

Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and…

We study QCD at non-zero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point \mu_c in agreement with that of chiral symmetry restoration computed with…

Supersymmetric vacua (`universes') of string/M theory may be identified with certain critical points of a holomorphic section (the `superpotential') of a Hermitian holomorphic line bundle over a complex manifold. An important physical…

We study the critical frontiers of the Potts model on two-dimensional bow-tie lattices with fully inhomogeneous coupling constants. Generally, for the Potts critical frontier to be found exactly, the underlying lattice must be a 3-uniform…

We compute the critical polymials for the q-state Potts model on all Archimedean lattices, using a parallel implementation of the algorithm of (Jacobsen, J. Phys. A: Math. Theor. 47 135001) that gives us access to larger sizes than…