Extension of the path-probability method beyond the pair approximation. Triangle approximation

Global entanglement and quantum phase transitions in the transverse XY Heisenberg chain

“…This allows us to obtain the exponent ν, which governs the divergence of the correlation length as dEg dh ∼ |h−1| −ν with ν = 1/2, consistent with previous reports [31,32].…”

“…As can be seen in Fig. (4), all the curves of F = 1 − exp[ dEg dλ − dEg dλ | λ=λm ] as a function of N 1/ν (λ − λ m ) collapse nicely on a single curve for ν = 1, in agreement with the well known result for the Ising universality class [28,32]. We finally note that our results was obtained for r = 0.5, however, similar results hold for 0 < r ≤ 1…”

The effect of Pd on the isothermal relaxation of short-range order in Au(Ag)-based ternary alloys

“…2 shows that the single exponential law and the log-normal distribution of relaxation time [13] does not fit the data and are too simple to describe the SROrelaxation here. Therefore, we apply the sum of exponentials law [14][15][16] to the present measurements. The least-squares fitting of the resistivity data was done using the non-linear regression method [17].…”

Ordering Kinetics and Diffusion in Some L12 Alloys

“…Theories extant up to 1973 were comprehensively reviewed by Yamauchi and de Fontaine (1974). The most thorough attempt on these lines is that due to Sato, Kikuchi and Gschwend (Sato and Kikuchi, 1976;Gschwend et al, 1978Gschwend et al, , 1979McCoy et al, 1982) which introduced two innovations: the presumption of the primary role of vacancy diffusion and the computation of the most probable path for the change of configuration, using the cluster variation approach. This family of treatments is generally termed the path probability method (PPM) approach.…”