论文标题
精确解决加权部分定向的步行，穿过正方形
Exact solution of weighted partially directed walks crossing a square
论文作者
论文摘要
我们认为部分定向的步行是跨越$ l \ times l $ square的长度，其长度通过奢侈的$ t $。该模型的确切解决方案以三种不同的方式计算，具体取决于$ t $是小于，等于还是大于1。在所有情况下，计算了分区函数的主要渐近行为的完整表达。该模型承认了稀释的密度相变，其中$ 0 <t <1 $，分区函数以$ l $成倍的缩放为$ l $，而对于$ t> 1 $，分区函数以$ l^2 $成倍的缩放，而当$ t = 1 $时，则有一个中间缩放率，在$ l \ log log \ log \ log \ l \ l} $ {l} $中是指数的。
We consider partially directed walks crossing a $L\times L$ square weighted according to their length by a fugacity $t$. The exact solution of this model is computed in three different ways, depending on whether $t$ is less than, equal to or greater than 1. In all cases a complete expression for the dominant asymptotic behaviour of the partition function is calculated. The model admits a dilute to dense phase transition, where for $0 < t < 1$ the partition function scales exponentially in $L$ whereas for $t>1$ the partition function scales exponentially in $L^2$, and when $t=1$ there is an intermediate scaling which is exponential in $L \log{L}$.
