The McCoy-Wu Model in the Mean-field Approximation

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents $\beta \approx 3.6$ and $\beta_1 \approx 4.1$ in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent $\alpha \approx -3.1$. The samples reduced critical temperature $t_c=T_c^{av}-T_c$ has a power law distribution $P(t_c) \sim t_c^{\omega}$ and we show that the difference between the values of the critical exponents in the pure and in the random system is just $\omega \approx 3.1$. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.Comment: LaTeX file with iop macros, 13 pages, 7 eps figures, to appear in J. Phys.

The Random-bond Potts model in the large-q limit

We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal properties of which are related to the critical singularities of the random Potts model. The optimization problem of finding the dominant graph, is studied on the square lattice by simulated annealing and by a combinatorial algorithm. Critical exponents of the magnetization and the correlation length are estimated and conformal predictions are compared with numerical results.Comment: 7 pages, 6 figure

Surface critical behavior of random systems at the ordinary transition

We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation, as well as in $d=4-\epsilon$ dimensions. At $d=4-\epsilon$ we extend, up to the next-to-leading order, the previous first-order results of the $\sqrt{\epsilon}$ expansion by Ohno and Okabe [Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface exponents are computed using Pade approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.Comment: 11 pages, 11 figure

Different species of legumes grown in combination with oats as green forage

Green fodder mixture trials were carried out with GK Impala, a winter hardy, fall sown oat variety registered in 2005 intercropped either with winter vetch or winter pea in a crop year when the spring was dry (2003) and in another one (2004) when the precipitation was optimal in spring. The two components of mixtures were sown 50% each. A four-replicate randomised complete block design was used with 50 m2 plots. The results were compared to the mixtures of spring oats and vetch; and spring oats and pea, respectively. The green matter of fall sown crops was cut by scythe late May, whereas that of spring crops early June.Data demonstrate that the green forage yield and protein production of fall sown oats as a monocrop and intercropped with vetch was higher than those of spring types. Green matter and dry matter yield varied with season, and were more advantageous in the year 2004, when there was more precipitation. The crude protein content of winter vetch and the crude protein production of the mixture fall sown oats + winter vetch were the highest. The mixtures with winter or spring pea yielded less green matter and, as a matter of fact, less crude protein. The fodder mixtures cereals — legumes are conventionally and widely used as feed for livestock in North-America, and the results of our two-year experiment suggest that their use should be intensified in Hungary as well, mainly in the provisional feeding of ruminants. To date, oat varieties with reliable winter hardiness are offered for fall sowing