THE SOLUTION OF THE THREE-DIMENSIONAL TWISTED GROUP LATTICES

1992 ◽  
Vol 06 (10) ◽  
pp. 1631-1645 ◽  
Author(s):  
STUART SAMUEL
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Group Representations ◽  
Screw Dislocations ◽  
Irreducible Group ◽  
Twisted Group ◽  
Free Propagation

We define new lattices called d-dimensional twisted group lattices. They are similar to ordinary lattices except that abstract screw dislocations are present at the centers of all plaquettes. Some physical aspects are enumerated. We consider the statistical mechanics system of free propagation on the three-dimensional twisted group lattice. For this case, the partition function is explicitly computed by finding the irreducible group representations.

scholarly journals Order-disorder statistics. I

1949 ◽  
Vol 196 (1044) ◽  
pp. 36-50 ◽  
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Infinite Matrix ◽  
Characteristic Structure ◽  
Single Function ◽  
Simple Characteristic ◽  
Distant Neighbour ◽  
Function Of Two Variables

In 1941 Kramers & Wannier discussed the statistical mechanics of a two-dimensional Ising model of a ferromagnetic. By making use of a ‘screw transformation’ they showed that the partition function was the largest eigenvalue of an infinite matrix of simple characteristic structure. In the present paper an alternative method is used for deriving the partition function, and this enables the ‘screw transformation’ to be generalized to apply to a number of problems of classical statistical mechanics, including the three-dimensional Ising model. Distant neighbour interactions can also be taken into account. The relation between the ferromagnetic and order-disorder problems is discussed, and it is shown that the partition function in both cases can be derived from a single function of two variables. Since distant neighbour interactions can be taken into account the theory can be formally applied to the statistical mechanics of a system of identical particles.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

scholarly journals BOSE–FERMI EQUIVALENCE IN THREE-DIMENSIONAL NONCOMMUTATIVE SPACETIME

2008 ◽  
Vol 23 (35) ◽  
pp. 3015-3022
Author(s):  
K. M. AJITH ◽  
E. HARIKUMAR ◽  
M. SIVAKUMAR
Keyword(s):  
Partition Function ◽  
Gauge Field ◽  
Three Dimensional ◽  
Coupling Constant ◽  
Spin Factor ◽  
Noncommutative Spacetime ◽  
Chern Simons

We study the fermionisation of Seiberg–Witten mapped action (to order θ) of the λϕ4 theory coupled minimally with U(1) gauge field governed by Chern–Simons action. Starting from the corresponding partition function we derive nonperturbatively (in coupling constant) the partition function of the spin-1/2 theory following Polyakov spin factor formalism. We find that the dual interacting fermionic theory is nonlocal. This feature also persists in the limit of vanishing self-coupling. In θ → 0 limit, the commutative result is obtained.

scholarly journals Hard Squares with Negative Activity and Rhombus Tilings of the Plane

10.37236/1093 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Jakob Jonsson
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Simplicial Complex ◽  
Transfer Matrix ◽  
Euler Characteristic ◽  
Independent Sets ◽  
Roots Of Unity ◽  
Hard Squares ◽  
Vertex Set

Let $S_{m,n}$ be the graph on the vertex set ${\Bbb Z}_m \times {\Bbb Z}_n$ in which there is an edge between $(a,b)$ and $(c,d)$ if and only if either $(a,b) = (c,d\pm 1)$ or $(a,b) = (c \pm 1,d)$ modulo $(m,n)$. We present a formula for the Euler characteristic of the simplicial complex $\Sigma_{m,n}$ of independent sets in $S_{m,n}$. In particular, we show that the unreduced Euler characteristic of $\Sigma_{m,n}$ vanishes whenever $m$ and $n$ are coprime, thereby settling a conjecture in statistical mechanics due to Fendley, Schoutens and van Eerten. For general $m$ and $n$, we relate the Euler characteristic of $\Sigma_{m,n}$ to certain periodic rhombus tilings of the plane. Using this correspondence, we settle another conjecture due to Fendley et al., which states that all roots of $\det (xI-T_m)$ are roots of unity, where $T_m$ is a certain transfer matrix associated to $\{\Sigma_{m,n} : n \ge 1\}$. In the language of statistical mechanics, the reduced Euler characteristic of $\Sigma_{m,n}$ coincides with minus the partition function of the corresponding hard square model with activity $-1$.

scholarly journals Statistical Mechanics of Discrete Multicomponent Fragmentation

2020 ◽  
Vol 5 (4) ◽  
pp. 64
Author(s):  
Themis Matsoukas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Closed Form ◽  
Fixed Number ◽  
Arbitrary Degree ◽  
Fragment Distribution ◽  
The Mean ◽  
Fragmentation Event

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity, and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation, and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory

1983 ◽  
Vol 272 ◽  
pp. 301 ◽  
Author(s):  
J. J. Macfarlane ◽  
W. B. Hubbard
Keyword(s):  
High Pressure ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Light Elements ◽  
Dirac Theory ◽  
Thomas Fermi
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