172 research outputs found
"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
Soluble kagome Ising model in a magnetic field
An Ising model on the kagome lattice with super-exchange interactions is
solved exactly under the presence of a nonzero external magnetic field. The
model generalizes the super-exchange model introduced by Fisher in 1960 and is
analyzed in light of a free-fermion model. We deduce the critical condition and
present detailed analyses of its thermodynamic and magnetic properties. The
system is found to exhibit a second-order transition with logarithmic
singularities at criticality.Comment: 8 pages, 8 figures, references adde
Critical frontier of the Potts and percolation models in triangular-type and kagome-type lattices I: Closed-form expressions
We consider the Potts model and the related bond, site, and mixed site-bond
percolation problems on triangular-type and kagome-type lattices, and derive
closed-form expressions for the critical frontier. For triangular-type lattices
the critical frontier is known, usually derived from a duality consideration in
conjunction with the assumption of a unique transition. Our analysis, however,
is rigorous and based on an established result without the need of a uniqueness
assumption, thus firmly establishing all derived results. For kagome-type
lattices the exact critical frontier is not known. We derive a closed-form
expression for the Potts critical frontier by making use of a homogeneity
assumption. The closed-form expression is new, and we apply it to a host of
problems including site, bond, and mixed site-bond percolation on various
lattices. It yields exact thresholds for site percolation on kagome, martini,
and other lattices, and is highly accurate numerically in other applications
when compared to numerical determination.Comment: 22 pages, 13 figure
Exact solution of the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice
A star-triangle mapping transformation is used to establish an exact
correspondence between the spin-1/2 Ising model on the Shastry-Sutherland
(orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a
bathroom tile (4-8) lattice. Exact results for the critical temperature and
spontaneous magnetization are obtained and compared with corresponding results
on the regular Ising lattices.Comment: 8 pages, 4 figure
Quantum Field Induced Orderings in Fully Frustrated Ising Spin Systems
We study ordering mechanisms which are induced by the quantum fluctuation in
fully frustrated Ising spin systems. Since there are many degenerated states in
frustrated systems, "order by thermal disorder" often takes place due to a kind
of entropy effect. To consider "order by quantum disorder" in fully frustrated
Ising spin systems, we apply transverse field as quantum fluctuation. There
exists a ferromagnetic correlation in each sublattice. The sublattice
correlation at zero temperature is enlarged due to transverse field. The
quantum fluctuation enhances the solid order at zero temperatures. This is an
example of quantum field induced ordering in fully frustrated systems. We also
study a case in which the transverse field induces a reentrant behavior as
another type of order by quantum disorder, and compare correspondent cases in
the classical systems.Comment: 3 pages, 4 figures, submitted to Proceedings of Symposia "Nanoscience
and Quantum Physics
Thermodynamic properties of the exactly solvable transverse Ising model on decorated planar lattices
The generalized mapping transformation technique is used to obtain the exact
solution for the transverse Ising model on decorated planar lattices. Within
this scheme, the basic thermodynamic quantities are calculated for different
planar lattices with arbitrary spins of decorating atoms. The particular
attention has been paid to the investigation of the transverse-field effects on
magnetic properties of the system under investigation. The most interesting
numerical results for the phase diagrams, compensation temperatures and several
thermodynamic quantities are discussed in detail for the ferrimagnetic version
of the model.Comment: 9 pages, 13 figures, submitted to Journal of Magnetism and Magnetic
Material
Exactly solvable mixed-spin Ising-Heisenberg diamond chain with the biquadratic interactions and single-ion anisotropy
An exactly solvable variant of mixed spin-(1/2,1) Ising-Heisenberg diamond
chain is considered. Vertical spin-1 dimers are taken as quantum ones with
Heisenberg bilinear and biquadratic interactions and with single-ion
anisotropy, while all interactions between spin-1 and spin-1/2 residing on the
intermediate sites are taken in the Ising form. The detailed analysis of the
ground state phase diagram is presented. The phase diagrams have shown to
be rather rich, demonstrating large variety of ground states: saturated one,
three ferrimagnetic with magnetization equal to 3/5 and another four
ferrimagnetic ground states with magnetization equal to 1/5. There are also two
frustrated macroscopically degenerated ground states which could exist at zero
magnetic filed.
Solving the model exactly within classical transfer-matrix formalism we
obtain an exact expressions for all thermodynamic function of the system. The
thermodynamic properties of the model have been described exactly by exact
calculation of partition function within the direct classical transfer-matrix
formalism, the entries of transfer matrix, in their turn, contain the
information about quantum states of vertical spin-1 XXZ dimer (eigenvalues of
local hamiltonian for vertical link).Comment: 14 pages, 9 figure
Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices
Using exact results, we determine the complex-temperature phase diagrams of
the 2D Ising model on three regular heteropolygonal lattices, (kagom\'{e}), , and (bathroom
tile), where the notation denotes the regular -sided polygons adjacent to
each vertex. We also work out the exact complex-temperature singularities of
the spontaneous magnetisation. A comparison with the properties on the square,
triangular, and hexagonal lattices is given. In particular, we find the first
case where, even for isotropic spin-spin exchange couplings, the nontrivial
non-analyticities of the free energy of the Ising model lie in a
two-dimensional, rather than one-dimensional, algebraic variety in the
plane.Comment: 31 pages, latex, postscript figure
分光光度計によるプランクトン色素の研究―3 : 植物プランクトン色素量とポピュレイション消長との関係(1959年の場合)
Succeeding to two previous reports, we tried to elucidate the relation between cell number and E670-value in this report. From a view point monthly, proportionality existed between them generally (Tab. 1) but in each case the relation was not always so, for the relation was differnt considerably in every sample (Fig. 1). Therefore, to analyse in detail. the authors showed figures (Fig. 2 & 3) of the relation between cell number and E670-value per one cell, in stead of E670-value, and knew that the relation was hyperbolic (Fig. 2), experimental equation being linear in logarithmic expression (Fig. 3). But circumstances are differ by cell number; i. e. in the case of cell number less than 300,000 cells per liter, the more cell number per liter we observe the less E₆₇₀-value per one cell we obtain. The experimental equation is log y₂=-0.9675logx+3.6258 where x is cell number per liter and y₂ is E₆₇₀-value per one cell, determined by the method already described in the previous reports. Consequently. it will be clear that the less cell number per liter we observe the more E₆₇₀-value per one cell we obtain; this is, minimum cell number agrees with maximum E₆₇₀-value per one cell. Therefore, in the coastal region, the authors guessed that during the plankton desert period or interval term of the two succeeding prosperities of population E₆₇₀-value per one cell becomes rather plentiful
Exact critical points of the O() loop model on the martini and the 3-12 lattices
We derive the exact critical line of the O() loop model on the martini
lattice as a function of the loop weight .A finite-size scaling analysis
based on transfer matrix calculations is also performed.The numerical results
coincide with the theoretical predictions with an accuracy up to 9 decimal
places. In the limit , this gives the exact connective constant
of self-avoiding walks on the martini lattice. Using
similar numerical methods, we also study the O() loop model on the 3-12
lattice. We obtain similarly precise agreement with the exact critical points
given by Batchelor [J. Stat. Phys. 92, 1203 (1998)].Comment: 4 pages, 3 figures, 2 table
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