Self-avoiding walk in five or more dimensions I. The critical behaviour
نویسندگان
چکیده
منابع مشابه
Critical Behaviour of Self-avoiding Walk in Five or More Dimensions
We use the lace expansion to prove that in five or more dimensions the standard self-avoiding walk on the hypercubic (integer) lattice behaves in many respects like the simple random walk. In particular, it is shown that the leading asymptotic behaviour of the number of «-step self-avoiding walks is purely exponential, that the mean square displacement is asymptotically linear in the number of ...
متن کاملThe Self-Avoiding-Walk and Percolation Critical Points in High Dimensions
We prove existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on Z d . For the critical point, de ned to be the reciprocal of the connective constant, the coe cients of the expansion are computed through order d 6 , with a rigorous error bound of order d 7 . Our method for computing terms in the expansion also applies ...
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We consider self-avoiding walk and percolation in Zd, oriented percolation in Z×Z+, and the contact process in Zd, with pD( · ) being the coupling function whose range is denoted by L < ∞. For percolation, for example, each bond {x, y} is occupied with probability pD(y−x). The above models are known to exhibit a phase transition when the parameter p varies around a model-dependent critical poin...
متن کاملCritical points for spread - out self - avoiding walk , percolation and the contact process above the upper critical dimensions
We consider self-avoiding walk and percolation in Zd, oriented percolation in Z×Z+, and the contact process in Zd, with p D( · ) being the coupling function whose range is denoted by L < ∞. For percolation, for example, each bond {x, y} is occupied with probability p D(y−x). The above models are known to exhibit a phase transition when the parameter p varies around a model-dependent critical po...
متن کاملTwo dimensional self-avoiding walk with hydrogen-like bonding: Phase diagram and critical behaviour
The phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model displays a collapse transition. In contrast to the standard θ-point model, the transition is first order. The phase diagram in the full fugacity-temperature pla...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1992
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02099530