Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userStochastic $phi^4-$Theory in the Strong Coupling Limit
357
0
0.0
(
0
)
Added by
Alireza Bahraminasab
Publication date
2006
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The stochastic $phi^4$-theory in $d-$dimensions dynamically develops domain wall structures within which the order parameter is not continuous. We develop a statistical theory for the $phi^4$-theory driven with a random forcing which is white in time and Gaussian-correlated in space. A master equation is derived for the probability density function (PDF) of the order parameter, when the forcing correlation length is much smaller than the system size, but much larger than the typical width of the domain walls. Moreover, exact expressions for the one-point PDF and all the moments $<phi^n>$ are given. We then investigate the intermittency issue in the strong coupling limit, and derive the tail of the PDF of the increments $phi(x_2) - phi(x_1)$. The scaling laws for the structure functions of the increments are obtained through numerical simulations. It is shown that the moments of field increments defined by, $C_b=< |phi(x_2)-phi(x_1)|^b>$, behave as $|x_1-x_2|^{xi_b}$, where $xi_b=b$ for $bleq 1$, and $xi_b=1$ for $bgeq1$
rate research
Read More
In this contribution we present an exploratory study of several novel methods for numerical stochastic perturbation theory. For the investigation we consider observables defined through the gradient flow in the simple {phi}^4 theory.
We make a detailed analysis of the spontaneous $Z_{2}$-symmetry breaking in the two dimensional real $phi^{4}$ theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the physical observables without statistical uncertainties. We determine the critical coupling in the continuum limit employing the tensor network formulation for scalar field theories proposed in our previous paper. We obtain $left[ lambda / mu_{mathrm{c}}^{2} right]_{mathrm{cont.}} = 10.913(56)$ with the quartic coupling $lambda$ and the renormalized critical mass $mu_{mathrm{c}}$. The result is compared with previous results obtained by different approaches.
We show that the exact beta-function beta(g) in the continuous 2D gPhi^{4} model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation tilde{g}=d(g) such that beta(d(g))=d(g)beta(g) is constructed and the approximate values of g^{*} computed from the duality equation d(g^{*})=g^{*} are shown to agree with the available numerical results. The calculation of the beta-function beta(g) for the 2D scalar gPhi^{4} field theory based on the strong coupling expansion is developed and the expansion of beta(g) in powers of g^{-1} is obtained up to order g^{-8}. The numerical values calculated for the renormalized coupling constant g_{+}^{*} are in reasonable good agreement with the best modern estimates recently obtained from the high-temperature series expansion and with those known from the perturbative four-loop renormalization-group calculations. The application of Cardys theorem for calculating the renormalized isothermal coupling constant g_{c} of the 2D Ising model and the related universal critical amplitudes is also discussed.
We determine universal critical exponents that describe the continuous phase transitions in different dimensions of space. We use continued functions without any external unknown parameters to obtain analytic continuation for the recently derived 7- loop $epsilon$ expansion from $O(n)$-symmetric $phi^4$ field theory. Employing a new blended continued function, we obtain critical exponent $alpha=-0.0121(22)$ for the phase transition of superfluid helium which matches closely with the most accurate experimental value. This result addresses the long-standing discrepancy between the theoretical predictions and precise experimental result of $O(2)$ $phi^4$ model known as $lambda$-point specific heat experimental anomaly. Further we have also examined the applicability of such continued functions in other examples of field theories.
We analyze the quantum phase diagram of the Holstein-Hubbard model using an asymptotically exact strong-coupling expansion. We find all sorts of interesting phases including a pair-density wave (PDW), a charge 4e (and even a charge 6e) superconductor, regimes of phase separation, and a variety of distinct charge-density-wave (CDW), spin-density-wave (SDW) and superconducting regimes. We chart the crossovers that occur as a function of the degree of retardation, i.e. the ratio of characteristic phonon frequency to the strength of interactions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
