scholarly journals THE FOURTH VIRIAL COEFFICIENT OF ANYONS

1998 ◽  
Vol 13 (21) ◽  
pp. 3723-3747 ◽  
Author(s):  
ANDERS KRISTOFFERSEN ◽  
STEFAN MASHKEVICH ◽  
JAN MYRHEM ◽  
KÅRE OLAUSSEN
Keyword(s):  
Monte Carlo ◽  
Fourier Series ◽  
Monte Carlo Method ◽  
Path Integral ◽  
Virial Coefficient ◽  
Path Integrals ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Partition Functions ◽  
Two Dimensional

We have computed by a Monte Carlo method the fourth virial coefficient of free anyons, as a function of the statistics angle θ. It can be fitted by a four term Fourier series, in which two coefficients are fixed by the known perturbative results at the boson and fermion points. We compute partition functions by means of path integrals, which we represent diagramatically in such a way that the connected diagrams give the cluster coefficients. This provides a general proof that all cluster and virial coefficients are finite. We give explicit polynomial approximations for all path integral contributions to all cluster coefficients, implying that only the second virial coefficient is statistics dependent, as is the case for two-dimensional exclusion statistics. The assumption leading to these approximations is that the tree diagrams dominate and factorize.

scholarly journals GENERALIZED PARTITION FUNCTIONS, INTERPOLATING STATISTICS AND HIGHER VIRIAL COEFFICIENTS

1999 ◽  
Vol 14 (18) ◽  
pp. 1217-1226 ◽  
Author(s):  
P. F. BORGES ◽  
H. BOSCHI-FILHO ◽  
C. FARINA
Keyword(s):  
Boundary Condition ◽  
Finite Temperature ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Partition Functions ◽  
Generalized Partition

Starting from determinants at finite temperature obeying an intermediate boundary condition between the periodic (bosonic) and antiperiodic (fermionic) cases, we find results which can be mapped onto those obtained from anyons for the second virial coefficient. Using this approach, we calculate the corresponding higher virial coefficients and compare them with the results in the literature.

Structures and crystallization of vacuum-deposited amorphous Se and Sb films

1990 ◽  
Vol 48 (4) ◽  
pp. 140-141
Author(s):  
Makoto Shiojiri ◽  
Toshiyuki Isshiki ◽  
Tetsuya Fudaba ◽  
Yoshihiro Hirota
Keyword(s):  
Monte Carlo ◽  
Electron Microscope ◽  
Monte Carlo Method ◽  
Computer Program ◽  
Radial Distribution ◽  
Film Formation ◽  
Amorphous State ◽  
Two Dimensional ◽  
Amorphous Films ◽  
Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

TI/PIMC METHOD WITH THE TAKAHASHI–IMADA APPROXIMATION FOR THE EQUILIBRIUM CONSTANT OF THE O + HCl ⇌ OH + Cl REACTION

2013 ◽  
Vol 12 (04) ◽  
pp. 1350026 ◽  
Author(s):  
MARCIN BUCHOWIECKI
Keyword(s):  
Monte Carlo ◽  
Temperature Dependence ◽  
Equilibrium Constant ◽  
Path Integral ◽  
Thermodynamic Integration ◽  
Partition Functions ◽  
Integration Path ◽  
Path Integral Monte Carlo

The thermodynamic integration/path integral Monte Carlo (TI/PIMC) method of calculating the temperature dependence of the equilibrium constant quantum mechanically is applied to O + HCl ⇌ OH + Cl reaction. The method is based upon PIMC simulations for energies of the reactants and the products and subsequently on thermodynamic integration for the ratios of partition functions. PIMC calculations are performed with the primitive approximation (PA) and the Takahashi–Imada approximation (TIA).

The second virial coefficients of mixed polar vapours

1959 ◽  
Vol 249 (1258) ◽  
pp. 414-426 ◽  
Keyword(s):  
Methyl Acetate ◽  
Virial Coefficient ◽  
Methyl Formate ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Ethyl Formate ◽  
Carbonyl Oxygen ◽  
Second Virial Coefficients ◽  
Theoretical Significance ◽  
Boyle’S Law

The second virial coefficients of binary mixtures of chloroform with methyl formate, n -propyl formate, methyl acetate, ethyl acetate and diethylamine have been measured in a ‘Boyle’s law apparatus’ at temperatures between 50 and 95 °C. The measured values are consistently higher than predicted by the theory of corresponding states, and a quantitative interpretation is proposed, based on the hypothesis that the esters and amine are partially dimerized and are involved in association with the chloroform by hydrogen bonding. A linear relation is shown to exist between the heats and entropies of association for the various mixtures, and the theoretical significance of this is discussed. There is some evidence that hydrogen bonds are formed through the alkoxyl oxygen by formate esters and through the carbonyl oxygen by acetate esters. The paper includes data on the second virial coefficient for the pure esters and for ethyl formate and methyl propionate.

Concentration Phase Transition in a Two-Dimensional Ferromagnet

2020 ◽  
Vol 312 ◽  
pp. 244-250
Author(s):  
Alexander Konstantinovich Chepak ◽  
Leonid Lazarevich Afremov ◽  
Alexander Yuryevich Mironenko
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermal Effect ◽  
Spin State ◽  
Critical Concentration ◽  
Two Dimensional ◽  
Percolation Transition ◽  
Magnetic Cluster ◽  
The Monte Carlo Method

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

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