磁性与韦氏交换场——基于最新实验的理论分析

我们解释了最近实验中观察到的自旋极快预cession频率的原因，即电子自旋与薄膜中所谓韦氏交换场之间的鞋氏耦合。提出了电子在非均匀交换场中运动的“电子斯特恩-格拉赫实验”。阐述了交换相互作用及大尺度交换场的微观来源，进而导致不同的磁性有序类型。presented a microscopic derivation of the equations of motion of the Weiss exchange field. Novel proofs of the existence of phase transitions in quantum XY-models and antiferromagnets, based on an analysis of the statistical distribution of the exchange field, are outlined. We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into two different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees, but the other is {\it not yet} bond driven and does not contain the Derrida-Herrmann model as special point. Instead it ends at a multicritical point $P^*$ where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. The Derrida-Herrmann model is representative for the bond driven collapse, which then forms the fourth universality class on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.