Broad histogram method for multiparametric Hamiltonians

Abstract

We extended the Broad Histogram Method in order to obtain spectral degeneracies for systems with multiparametric Hamiltonians. As examples we obtained the critical lines for the square lattice Ising model with nearest and next-nearest neighbor interactions and the antiferromagnetic Ising model in an external field. For each system, the entire critical line is obtained using data from a single computer run. We also discuss the accuracy and efficiency of our method.PACS numbers: 02.70.Lq, 05.50.+q, 75.10.HkThe search for new and more efficient methods for computer simulations is always an intensive task in science. Multispin coding techniques (see [1] and references therein), cluster algorithms [2,3,4], reweighting procedures [5,6,7] and methods which calculate directly the spectral degeneracy [8, 9, 10, 11] are a few remarkable examples (see [12,13,14] for reviews). An efficient implementation of these methods can lead to an enormous increase in speed and accuracy of computer simulations. Multiparametric simulation is another way to further improve the efficiency.Multiparametric simulations allow, from a single computer run, to explore the whole space of parameters defining a given system, instead of repeating the whole process every time some parameter is changed.

Phase diagram of the 3D bimodal random-field Ising model

“…We will now be recording, again in the high-levels of the WL diffusion process, the cumu-lative (exchange-energy, field-energy) two-parametric histograms, in order to produce an approximation for the two-parametric DOS of the RFIM. At this point, we should stress that any multi-parametric WL process is inevitably restricted to rather small lattices [62,74,75,76,77]. In fact the applications of such multi-parametric methods are substantially limited, since besides the immense time and excessive memory requirements, they very often face severe ergodic and/or convergence problems, depending on both the physical system and the algorithmic implementation.…”

Electrical characterization of the [N(CH3)4][N(C2H5)4]ZnCl4 compound

“…The title compound of [N(CH 3 ) 4 ][N(C 2 H 5 ) 4 ]ZnCl 4 was synthesized starting from precursor N(CH 3 ) 4 Cl, N (C 2 H 5 ) 4 Cl, and ZnCl 2 of high purity (more than 99.9%). The precursors were weighted in the stoichiometric proportion in conformity with the following equation, then dissolved in a minimum quantity of water and finally mixed.…”

“…The crystal structure of the [N(CH 3 ) 4 ][N(C 2 H 5 ) 4 ]ZnCl 4 compound can be described by alternating organic layers (TEA) 2+ and organic-inorganic layers [(TMA) + /ZnCl 4 2− ] parallel to the (0 1 0) plane (Fig. 1).…”

“…[N(C 2 H 5 ) 4 ][NCH3 )4 ]ZnCl 4 compound is investigated in the temperature range 420-520 K. The X-ray diffraction analysis shows that the compound crystallizes in an orthorhombic system. The Raman and infrared spectra of the [(CH 3 ) 4 N][(C 2 H 5 ) 4 N]ZnCl 4 compound can be divided into three parts: the vibrational modes of [ZnCl 4 ] 2− below 300 cm −1 , the internal modes of the [(CH 3 ) 4 N] + , and the [(C 2 H 5 ) 4 N] + cation in the 300-1000 cm −1 range and the vibrational modes of CH 3 and CH 2 above 1000 cm −1 .…”

Short-Time Dynamic Exponents of an Ising Model With Competing Interactions

“…1. From both numerical [2,11] and analytical [10,12] approaches, it was shown that in the plane of the reduced temperature kT /J 1 against the competition parameter −J 2 /J 1 , the phase diagram presents ferromagnetic, paramagnetic and super-antiferromagnetic phases. The critical line between the ferromagnetic and paramagnetic phases belongs to the universality class of the two-dimensional Ising model, whereas the critical exponents along the critical line separating the SAF ordered phase from the the paramagnetic phase are found to be non-universal.…”