318 research outputs found
Lifted Worm Algorithm for the Ising Model
We design an irreversible worm algorithm for the zero-field ferromagnetic
Ising model by using the lifting technique. We study the dynamic critical
behavior of an energy estimator on both the complete graph and toroidal grids,
and compare our findings with reversible algorithms such as the
Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm
algorithm improves the dynamic exponent of the energy estimator on the complete
graph, and leads to a significant constant improvement on toroidal grids.Comment: 9 pages, 6 figure
Approximating Pairwise Correlations in the Ising Model
In the Ising model, we consider the problem of estimating the covariance of the spins at two specified vertices. In the ferromagnetic case, it is easy to obtain an additive approx- imation to this covariance by repeatedly sampling from the relevant Gibbs distribution. However, we desire a multiplicative approximation, and it is not clear how to achieve this by sampling, given that the covariance can be exponentially small. Our main contribution is a fully polynomial time randomised approximation scheme (FPRAS) for the covariance in the ferromagnetic case. We also show that that the restriction to the ferromagnetic case is essential — there is no FPRAS for multiplicatively estimating the covariance of an antiferromagnetic Ising model unless RP = #P. In fact, we show that even determining the sign of the covariance is #P-hard in the antiferromagnetic case
Emergent Critical Properties in Liquid-Gas Transition and Single Dislocations in Solid He4
My research focuses on the analytical and numerical study of seemingly completely different systems - the classical critical point of the liquid-gas transition and a quantum topological defect (dislocation) in solid Helium-4. The unifying theme, though, is Emergence - the appearance of unexpected qualities at large distance and time scales in these systems. Our results resolve the long standing controversy about the nature of the liquid-gas criticality by showing with high confidence that it is the same as that of Ising ferromagnet. In solid 4He, a quantum superclimbing dislocation, which is expected to be violating space-time symmetry according to the elementary textbook assessment, shows emergence of this symmetry in our numerical simulations
Thermal denaturation of fluctuating finite DNA chains: the role of bending rigidity in bubble nucleation
Statistical DNA models available in the literature are often effective models
where the base-pair state only (unbroken or broken) is considered. Because of a
decrease by a factor of 30 of the effective bending rigidity of a sequence of
broken bonds, or bubble, compared to the double stranded state, the inclusion
of the molecular conformational degrees of freedom in a more general mesoscopic
model is needed. In this paper we do so by presenting a 1D Ising model, which
describes the internal base pair states, coupled to a discrete worm like chain
model describing the chain configurations [J. Palmeri, M. Manghi, and N.
Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is
exactly solved using a transfer matrix technique that presents an analogy with
the path integral treatment of a quantum two-state diatomic molecule. When the
chain fluctuations are integrated out, the denaturation transition temperature
and width emerge naturally as an explicit function of the model parameters of a
well defined Hamiltonian, revealing that the transition is driven by the
difference in bending (entropy dominated) free energy between bubble and
double-stranded segments. The calculated melting curve (fraction of open base
pairs) is in good agreement with the experimental melting profile of
polydA-polydT. The predicted variation of the mean-square-radius as a function
of temperature leads to a coherent novel explanation for the experimentally
observed thermal viscosity transition. Finally, the influence of the DNA strand
length is studied in detail, underlining the importance of finite size effects,
even for DNA made of several thousand base pairs.Comment: Latex, 28 pages pdf, 9 figure
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