814 research outputs found
Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models
Recently, we developed and implemented the bond propagation algorithm for
calculating the partition function and correlation functions of random bond
Ising models in two dimensions. The algorithm is the fastest available for
calculating these quantities near the percolation threshold. In this paper, we
show how to extend the bond propagation algorithm to directly calculate
thermodynamic functions by applying the algorithm to derivatives of the
partition function, and we derive explicit expressions for this transformation.
We also discuss variations of the original bond propagation procedure within
the larger context of Y-Delta-Y-reducibility and discuss the relation of this
class of algorithm to other algorithms developed for Ising systems. We conclude
with a discussion on the outlook for applying similar algorithms to other
models.Comment: 12 pages, 10 figures; submitte
The use of Lanczos's method to solve the large generalized symmetric definite eigenvalue problem
The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code
Time-Symmetric Rolling Tachyon Profile
We investigate the tachyon profile of a time-symmetric rolling tachyon
solution to open string field theory. We algebraically construct the solution
of [arXiv:0707.4472] at 6th order in the marginal parameter, and numerically
evaluate the corresponding tachyon profile as well as the action and several
correlation functions containing the equation of motion. We find that the
marginal operator's singular self-OPE is properly regularized and all
quantities we examine are finite. In contrast to the widely studied
time-asymmetric case, the solution depends nontrivially on the strength of the
deformation parameter. For example, we find that the number and period of
oscillations of the tachyon field changes as the strength of the marginal
deformation is increased. We use the recent renormalization scheme of
[arXiv:1412.3466], which contains two free parameters. At finite deformation
parameter the tachyon profile depends on these parameters, while when the
deformation parameter is small, the solution becomes insensitive to them and
behaves like previously studied time-asymmetric rolling tachyon solutions. We
also show that convergence of perturbation series is not as straightforward as
in the time-asymmetric case with regular OPE, and find evidence that it may
depend on the renormalization constants.Comment: 27 pages, 8 figures; reference added, extended discussion of
numerical integratio
"Exact" Algorithm for Random-Bond Ising Models in 2D
We present an efficient algorithm for calculating the properties of Ising
models in two dimensions, directly in the spin basis, without the need for
mapping to fermion or dimer models. The algorithm gives numerically exact
results for the partition function and correlation functions at a single
temperature on any planar network of N Ising spins in O(N^{3/2}) time or less.
The method can handle continuous or discrete bond disorder and is especially
efficient in the case of bond or site dilution, where it executes in O(L^2 ln
L) time near the percolation threshold. We demonstrate its feasibility on the
ferromagnetic Ising model and the +/- J random-bond Ising model (RBIM) and
discuss the regime of applicability in cases of full frustration such as the
Ising antiferromagnet on a triangular lattice.Comment: 4.2 pages, 5 figures, accepted for publication in Phys. Rev. Let
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