Surface reentrance in the semi-infinite spin-1 Ising models

The critical behavior of the semi-infinite Blume-Capel and Blume-Emery-Griffiths models is investigated in the pair approximation of the Cluster Variation Method. Equations for bulk and surface order parameters and n.n. correlation functions are given, from which analytical expressions for the second order bulk and surface critical temperatures are derived. The phase diagrams of the Blume-Capel model are classified, and the existence of a surface first order transition is discussed. This transition is shown to be, under certain conditions, slightly reentrant, and the behavior of the surface order parameters and correlation functions is given for such a case. The extension of our results to the Blume-Emery-Griffiths model is briefly discussed.Comment: 17 pages, 14 figures (PostScript, appended), POLFIS-TH.19/9

The Critical Behaviour of the Spin-3/2 Blume-Capel Model in Two Dimensions

The phase diagram of the spin-3/2 Blume-Capel model in two dimensions is explored by conventional finite-size scaling, conformal invariance and Monte Carlo simulations. The model in its $\tau$-continuum Hamiltonian version is also considered and compared with others spin-3/2 quantum chains. Our results indicate that differently from the standard spin-1 Blume-Capel model there is no multicritical point along the order-disorder transition line. This is in qualitative agreement with mean field prediction but in disagreement with previous approximate renormalization group calculations. We also presented new results for the spin-1 Blume-Capel model.Comment: latex 18 pages, 4 figure

Random-cluster representation of the Blume-Capel model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume--Capel model. It has three parameters, a vertex parameter $a$, an edge parameter $p$, and a cluster weighting factor $q$. Stochastic comparisons of measures are developed for the `vertex marginal' when $q\in[1,2]$, and the `edge marginal' when q\in[1,\oo). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume--Capel model

New universality class in three dimensions: The critical Blume-Capel model

We study the Blume-Capel universality class in $d=\frac{10}{3}-\epsilon$ dimensions. The RG flow is extracted by looking at poles in fractional dimension of three loop diagrams using $\overline{\rm MS}$. The theory is the only nontrivial universality class which admits an expansion to three dimensions with $\epsilon=\frac{1}{3}<1$. We compute the relevant scaling exponents and estimate some of the OPE coefficients to the leading order. Our findings agree with and complement CFT results. Finally we discuss a family of nonunitary multicritical models which includes the Lee-Yang and Blume-Capel classes as special cases.Comment: 5 pages, 1 figure, v2: new title, extended introduction, to appear in PR

Correlations equalities and some upper bounds for the critical temperature for spin one systems

Starting from correlation identities for the Blume-Capel spin 1 systems and using correlation inequalities, we obtain rigorous upper bounds for the critical temperature.The obtained results improve over effective field type results.Comment: 13 page

Keragaman Jenis Tumbuhan Di Cagar Alam Gunung Celering

Plant Diversity in the Mount Celering Nature Reserve. Titi Kalima and Nur M. Heriyanto. Study of the plant species diversity in the Nature Reserve of Mount Celering (CAGC) Jepara, Central Java, was carried out from April to May 2008, with aimed to get information about plant diversity after natural disasters and encroachment. The method used was the checkered path with length of 500 m and width of 20 m, made of three lines cut slopes. The research was found 32 species, 29 genera, and 21 families. Tree level was dominated by Hibiscus macrophyllus Roxb. (IVI = 26.75%), Artocarpus elasticus Blume (IVI = 26.53%), and Alseodaphne umbelliflora Blume. (IVI = 22.75%). Saplings by Syzygium acuminatissimum (Blume) A.DC. (IVI = 23.86%), Dipterocarpus hasseltii Blume (IVI = 18.71%), and Artocarpus elasticus Blume (IVI = 18.52%). Six species of endangered trees were Alstonia scholaris (L.) R.Br., Alstonia angustifolia Wall, D. hasseltii Blume, Parkia javanica (Lamk.) Merr., Stelechocarpus burahol Hk.f.et Th., Sterculia cordata Blume

Inventory of Terrestrial Orchids in the Baturraden Botanical Garden of Central Java

Baturraden Botanical Garden located on the slopes of Mount Slamet in the south has a high enough humidity so it is ideal for plant growth, especially orchids. As an ex-situ plant conservation area, the Baturraden Botanical Garden plays an important role in preserving the diversity of orchids in it. The purpose of this study was to find out the types and descriptions of terrestrial orchids in the Baturraden Botanical Garden area of Central Java. The method used in this study is a 400 m line transect method with an inter-point distance of 100 m each and data collection is carried out at 10 m each on the right and left of the line transect.  Hasil research shows that there are 13 species derived from 10 genus of soil orchids. The types that have been found are Goodyera rubicunda (Blume) Lindl., Calanthe pulchra (Blume) Lindl., Spathoglottis plicata Blume, Cryptostylis javanica J.J.Sm., Appendicula alba Blume, Phaius callosus (Blume) Lindl., Lepidogyne longifolia Blume, Tainia elongata J.J.Sm., Goodyera colorata Blume, Malaxis sp. Soland. ex Sw., Goodyera sp. R. Br., Goodyera procera (Ker-Gawl.) Hook., and Plocoglottis sp. Blume

Magnetic behavior of a spin-1 Blume-Emery-Griffiths model

I study the one-dimensional spin-1 Blume-Emery-Griffiths model with bilinear and biquadratic exchange interactions and single-ion crystal field under an applied magnetic field. This model can be exactly mapped into a tight-binding Hubbard model - extended to include intersite interactions - provided one renormalizes the chemical and the on-site potentials, which become temperature dependent. After this transformation, I provide the exact solution of the Blume-Emery-Griffiths model in one dimension by means of the Green's functions and equations of motion formalism. I investigate the magnetic variations of physical quantities - such as magnetization, quadrupolar moment, susceptibility - for different values of the interaction parameters and of the applied field, focusing on the role played by the biquadratic interaction in the breakdown of the magnetization plateaus.Comment: 4 pages, 5 figures. ICM 2009 (Karlsruhe) Conference proceeding

Critical behavior at edge singularities in one dimensional spin models

In ferromagnetic spin models above the critical temperature ($T > T_{cr}$) the partition function zeros accumulate at complex values of the magnetic field ($H_E$) with a universal behavior for the density of zeros \rho (H) \sim | H - H_E |^{\sg}. The critical exponent \sg is believed to be universal at each space dimension and it is related to the magnetic scaling exponent $y_h$ via \sg = (d-y_h)/y_h. In two dimensions we have y_h=12/5 (\sg = -1/6) while y_h=2 (\sg=-1/2) in $d=1$. For the one dimensional Blume-Capel and Blume-Emery-Griffiths models we show here, for different temperatures, that a new value y_h=3 (\sg =-2/3) can emerge if we have a triple degeneracy of the transfer matrix eigenvalues.Comment: to appear in Phys. Rev. E, 16 pages, 3 figure