We investigate the dual of the κ = 0 gonihedric Ising model on a 3D cubic lattice, which may be written as an anisotropically coupled Ashkin–Teller model. The original κ = 0 gonihedric model has a purely plaquette interaction, displays a first order transition and possesses a highly degenerate ground state. We find that the dual model admits a similar large ground state degeneracy as a result of the anisotropic couplings and investigate the coupled mean-field equations for the model on a single cube. We also carry out Monte Carlo simulations which confirm a first order phase transition in the model and suggest that the ground state degeneracy persists throughout the low temperature phase. Some exploratory cooling simulations also hint at non-trivial dynamical behaviour.
Abstract.The number of so-called invisible states which need to be added to the q-state Potts model to transmute its phase transition from continuous to first order has attracted recent attention. In the q = 2 case, a Bragg-Williams, mean-field approach necessitates four such invisible states while a 3-regular, random-graph formalism requires seventeen. In both of these cases, the changeover from second-to first-order behaviour induced by the invisible states is identified through the tricritical point of an equivalent BlumeEmery-Griffiths model.Here we investigate the generalised Potts model on a Bethe lattice with z neighbours. We show that, in the q = 2 case, r c (z) = 4z 3(z − 1)states are required to manifest the equivalent Blume-Emery-Griffiths tricriticality. When z = 3, the 3-regular, random-graph result is recovered, while z → ∞ delivers the Bragg-Williams, mean-field result.arXiv:1307.2803v1 [cond-mat.stat-mech]
The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2, 3, 4 and first order for higher q.Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions [1][2][3][4]. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed.In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs. arXiv:1303.0677v2 [cond-mat.stat-mech]
Sri Lanka is considered a highly fluctuating economy in the South Asian region. It is vital to understand the behavior of economy in order to obtain the maximum benefit. Stock market can be considered as one of the key influencers to the economy whereas the behavior of the stock market would highly define the behaviors of the overall economic system. It is required to identify the stock market measures and their contribution for the market development in order to identify the influence of stock market.The immense importance of its actions on the market performance leads to find more about the stock market’s measures. This research contains the evidence of the study conducted to identify the development of the stock market along with the behavior of the stock market measures such as all share price index, market capitalization, dividend yield, price to earnings ratio and shares traded equity. All of these variables were used to obtain a model to describe and predict performance of stock market over the time.This study is based on the secondary data obtained from the CSE (Colombo Stock Exchange). A trend analysis was conducted for each series of data and results were used for the analysis carried on from there. Unit root test was performed to ensure the stationarity of the data. Then, a time series regression model and Granger causality tests were used to identify the relationship between the measures of stock market. Major finding of the study depicts that all the measures of the stock market have influences on the stock market development except for the dividend yield. These findings are useful in the process of decision making in many aspects.
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