Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMinimal duality breaking in the Kallen-Lehman approach to 3D Ising model: a numerical test
174
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with MonteCarlo results by introducing a more general duality breaking is shortly discussed.
rate research
Read More
A phenomenological approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent {alpha} allow to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.
How can a renormalization group fixed point be scale invariant without being conformal? Polchinski (1988) showed that this may happen if the theory contains a virial current -- a non-conserved vector operator of dimension exactly $(d-1)$, whose divergence expresses the trace of the stress tensor. We point out that this scenario can be probed via lattice Monte Carlo simulations, using the critical 3d Ising model as an example. Our results put a lower bound $Delta_V>5.0$ on the scaling dimension of the lowest virial current candidate $V$, well above 2 expected for the true virial current. This implies that the critical 3d Ising model has no virial current, providing a structural explanation for the conformal invariance of the model.
We exploit the Kallen-Lehman representation of the two-point Green function to prove that the gluon propagator cannot go to zero in the infrared limit. We are able to derive also the functional form of it. This means that current results on the lattice can be used to derive the scalar glueball spectrum to be compared both with experiments and different aimed lattice computations.
The N-vector cubic model relevant, among others, to the physics of the randomly dilute Ising model is analyzed in arbitrary dimension by means of an exact renormalization-group equation. This study provides a unified picture of its critical physics between two and four dimensions. We give the critical exponents for the three-dimensional randomly dilute Ising model which are in good agreement with experimental and numerical data. The relevance of the cubic anisotropy in the O(N) model is also treated.
The ferromagnetic transition in the Ising model is the paradigmatic example of ergodicity breaking accompanied by symmetry breaking. It is routinely assumed that the thermodynamic limit is taken with free or periodic boundary conditions. More exotic symmetry-preserving boundary conditions, like cylindrical antiperiodic, are less frequently used for special tasks, such as the study of phase coexistence or the roughening of an interface. Here we show, instead, that when the thermodynamic limit is taken with these boundary conditions, a novel type of transition takes place below $T_c$ (the usual Ising transition temperature) without breaking neither ergodicity nor symmetry. Then, the low temperature phase is characterized by a regime (condensation) of strong magnetizations fluctuations which replaces the usual ferromagnetic ordering. This is due to critical correlations perduring for all T below Tc. The argument is developed exactly in the $d=1$ case and numerically in the d=2 case.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
