Phase Transitions of a Dilute O（n） Model

We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice with vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of thelattice. We apply a mapping of the spin degrees of freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of a continuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix.Our results reveal the existence of a tricritical line, parametrized by n, which connects the known universality classes of the tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of theIsing point,the tricritical line extends to the n = 2 point describing a tricritical O(2) model.

Experimental study on f-ω regulation model under abnormal methane emission

In view of the difficulty of automatic adjustment, the recovery lag and the major accident potential of the mine ventilation system, an experimental model of the pipe net was established according to the typical one mine and one working face ventilation system of Daliuta coal mine. Using the best uniform approximation method of Chebyshev interpolation to fit the fan performance curve, we experimentally determined fan characteristics with different frequencies and establish the data base for the curves. Based on ventilation network monitoring theory, we designed a monitoring system for ventilation network parameter monitoring and fan operating frequency automatic control. Using the absolute methane emission quantity to predict the air quantity requirement of branch and fan frequency, we established a f-ω regulation model based on fan frequency and absolute methane emission quantity. After analysing methane emission and distribution characteristics, using CO_2 to simulate the methane emission characteristics from a working face, we verified the correctness and rationality of the f-ω regulation model. The fan operation frequency is adjusted by the method of air adjustment change with methane emission quantity and the curve searching method after determining air quantity requirements. The results show that the air quantity in a branch strictly changes according to the f-ω regulation model, in the airincreasing dilution by fan frequency regulation, the CO_2 concentration is limited to the set threshold value. The paper verifies the practicability of a frequency regulation system and the feasibility of the frequency adjustment scheme and provides guidance for the construction of automatic frequency conversion control system in coal mine ventilation networks.

Magnetic phase diagrams of Fe–Mn–Al alloy on the Bethe lattice

The magnetic behaviors of the Fe–Mn–Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction（J） distribution in the Blume–Capel（BC） model. Ferromagnetic（J 〉 0） or antiferromagnetic（J 〈 0）bonds or dilution of the bonds（J = 0） are assumed between the atoms with some probabilities. It is found that the secondor the first-order phase boundaries separate the ferromagnetic（F）, antiferromagnetic（AF）, paramagnetic（P）, or spin-glass（SG） phases from the possible other one. In addition to the tricritical points, the special points at which the second- and the first-order and the spin-glass phase lines meet are also found. Very rich phase diagrams in agreement with the literature are obtained.