ANNUAL REPORT - MTA SzFKI

B. COMPLEX SYSTEMS
F. Iglói, R. Juhász, N. Menyhárd, A. Sütő, Zs. Szép, P. Szépfalusy
The principal interest of this group is the theoretical investigation of different aspects of
equilibrium and non-equilibrium statistical physics and quantum systems.
Phase transitions and critical behaviour. — We have studied the ferromagnetic large-q
state Potts model in complex evolving networks, which is equivalent to an optimal
cooperation problem, in which the agents try to optimize the total sum of pair cooperation
benefits and the supports of independent projects. The agents are found to be typically of
two kinds: a fraction of m (being the magnetization of the Potts model) belongs to a large
cooperating cluster, whereas the others are isolated one man's projects. It is shown
rigorously that the homogeneous model has a strongly first-order phase transition, which
turns to second-order for random interactions (benefits), the properties of which are
studied numerically on the Barabási-Albert network. The distribution of finite-size
transition points is characterized by a shift exponent, 1 ~ ν ′ = 0.26(1), and by a different
width exponent, 1 ν ′ = 0.18(1), whereas the magnetization at the transition point scales
with the size of the network, N, as:m ~ N x , with x = 0.66(1).
Large-scale Monte Carlo simulations were used to explore the effect of quenched disorder
on one-dimensional kinetic Ising models with locally broken spin symmetry. The model
was found to exhibit a continuous phase transition to an absorbing state. The associated
critical behavior is similar to that arising in the one-dimensional contact process with
Griffiths-like behavior. Variable cluster exponents were also found which obey the
hyperscaling law.
The dynamics and the structure factor of the helix-coil transition in the Poland-Scheraga
model of DNA-denaturation were studied. A universal scaling behavior was found in the
vicinity of the transition point, even when the transition is of first order. Predictions of
Langevin dynamics for the order parameter were shown to be in agreement with the results
of an evolution based on a microscopic dynamics and followed by Monte Carlo method.
In the leading order of the large N expansion to the SU(2) × O(N) globally symmetric
renormalizable scalar field theory symmetry-breaking solutions are found numerically
even when all fields have positive renormalized square mass. The symmetry breaking,
radiatively induced by the N-component hidden phantom field, can reproduce the standard
range of the electroweak condensate and of the Higgs mass.
In a one-loop parametrization of the SU(3) L × SU(3) R chiral quark model chiral
perturbation theory for mesons and baryons is used to study the boundary of the first order
phase transition region in the m π − m K − µ B space. The boundary surface of second order
phase transition points bends with increasing µ B towards the physical point of the mass
plane. At this point the scaling region of the critical end point (CEP) is explored.
Quantum systems. — We have studied the entanglement entropy of inhomogeneous
quantum systems. For the two-dimensional random transverse Ising model the
entanglement entropy is studied with a numerical implementation of the strong disorder
renormalization group. The asymptotic behavior of the entropy per surface area diverges
at, and only at, the quantum phase transition that is governed by an infinite randomness
fixed point. Here we identify a double-logarithmic multiplicative correction to the area law
for the entanglement entropy. This contrasts with the pure area law valid at the infinite
randomness fixed point in the diluted transverse Ising model in higher dimensions. We
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