324 research outputs found
Optimization Algorithms Based on Renormalization Group
Global changes of states are of crucial importance in optimization
algorithms. We review some heuristic algorithms in which global updates are
realized by a sort of real-space renormalization group transformation. Emphasis
is on the relationship between the structure of low-energy excitations and
``block-spins'' appearing in the algorithms. We also discuss the implication of
existence of a finite-temperature phase transition on the computational
complexity of the ground-state problem.Comment: 7 pages, 2 figure
Universal Jump in the Helicity Modulus of the Two-Dimensional Quantum XY Model
The helicity modulus of the S=1/2 XY model is precisely estimated through a
world line quantum Monte Carlo method enhanced by a cluster update algorithm.
The obtained estimates for various system sizes and temperatures are well
fitted by a scaling form with L replaced by \log(L/L_0), which is inferred from
the solution of the Kosterlitz renormalization group equation. The validity of
the Kosterlitz-Thouless theory for this model is confirmed.Comment: 4 pages, 3 figure
Phase Transition in Potts Model with Invisible States
We study phase transition in the ferromagnetic Potts model with invisible
states that are added as redundant states by mean-field calculation and Monte
Carlo simulation. Invisible states affect the entropy and the free energy,
although they do not contribute to the internal energy. The internal energy and
the number of degenerated ground states do not change, if invisible states are
introduced into the standard Potts model. A second-order phase transition takes
place at finite temperature in the standard -state ferromagnetic Potts model
on two-dimensional lattice for , and 4. However, our present model on
two-dimensional lattice undergoes a first-order phase transition with
spontaneous -fold symmetry breaking (, and 4) due to entropy effect
of invisible states. We believe that our present model is a fundamental model
for analysis of a first-order phase transition with spontaneous discrete
symmetry breaking.Comment: 8 pages, 4 figure
Supersolid of Hardcore Bosons on the Face Centered Cubic Lattice
We investigate a supersolid state in hardcore boson models on the
face-centered-cubic (FCC) lattice. The supersolid state is characterized by a
coexistence of crystalline order and superfluidity. Using a quantum Monte Carlo
method based on the directed-loop algorithm, we calculate static structure
factors and superfluid density at finite temperature, from which we obtain the
phase diagram. The supersolid phase exists at intermediate fillings between a
three-quarter-filled solid phase and a half-filled solid phase. We also discuss
the mechanism of the supersolid state on the FCC lattice.Comment: 5pages, 6figure
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