本文通过在加有边界场的一维横场伊辛模型的中间格点处加有一杂质，来研究其浸润相变。

在具有边界场的一维横场伊辛模型中，通常都设相邻格点间的最近邻相互作用为1.0，在本文中，我们设伊辛链中的中间格点与其前面一个格点间的近邻相互作用不等于1.0，通过这么一个很小的改变，我们来研究其链中的浸润相变。

首先，我们通过Jordan-Wigner变换将将伊辛链从泡利表象转换为Fock空间中无自旋的费米子系统，再用波戈流波夫变换将费米子系统的哈密顿量进行对角化，问题就演变成了一个求三对角的矩阵的本征值和本征态，通过一个程序包我们求出了该矩阵的本征值与本征态，然后根据这些本征值和本征态求出了体系的边界磁化强度和各个格点处的磁化强度。

我们设左边界场是一个正数，右边界场是负数，固定右边界场与杂质处的耦合系数，不断改变左边界场的值，来研究其相变。通过将三对角矩阵的久期方程不断按行和列来作展开，得出了该矩阵的局域态的本征值，以及其局域态存在的条件，我们令右边界场 =-1.0，以此来使右边界处没有局域态，再令左边界处的局域态的本征值与杂质处的局域态的本征值相等，得出了该体系的一个相变点。我们发现当左边界场时，体系的边界磁化强度有突变，故该相变点是一个一级相变点。

然后我们还通过程序算出了在该相变点附近，体系的不同格点处的磁化强度，并作出了图。结果显示，当从该相变点左边变到右边之后，体系的界面也从左边界突然移动到了中间点，即杂质存在的地方，因此它从非浸润相突变到了部分浸润相。

最后我们研究了体系的有限尺寸标度。我们先是作出了体系在一级相变点附近的不同尺寸的能隙图，然后将不同尺寸的能隙图像作坐标变换，发现不同尺寸的图像在作不同倍数的坐标变换之后，比较大的尺寸的能隙图像基本是重合在一起的，即它们的能隙满足同样的函数关系。最后我们还作出了不同尺寸体系在相变点处的能隙值与其尺寸间的关系图，以及它们的能隙在作坐标变换时，它们的横坐标的扩大倍数与其尺寸间的关系图。

在第五章中，我们做出了与取不同值的组合时，它们的边界磁化强度图以及磁化剖面图，我们了解了不同组合的界面在相变点附近的移动情况，以及杂质对界面的影响。

In this paper, an impurity is added to the middle lattice point of the one-dimensional transverse-field Ising model with a boundary field to study its wetting phase transition.

In the one-dimensional transverse-field Ising model with a boundary field, the nearest neighbor interaction between adjacent lattice points is usually set as 1.0. In this paper, we set the nearest neighbor interaction between the middle lattice point in the Ising chain and the previous lattice point is not equal to 1.0, and with such a small change, we study the wetting phase transition in its chain.

First, we convert the Ising chain from the Pauli representation to a spin-free Fermi system in Fock space through the Jordan-Wigner transformation, and then diagonalize the Hamiltonian of the Fermi system using the Bogoliubov transformation , the problem has evolved into finding the eigenvalues and eigenstates of a tridiagonal matrix. Through a program package, we found the eigenvalues and eigenstates of the matrix, and then based on these eigenvalues and eigenstates ,we obtains the boundary magnetization of the system and the magnetization at each lattice point.

We set the left boundary field to be a positive number and the right boundary field to be a negative number, fix the coupling coefficient of the impurity and the right boundary field , and constantly change the value of the left boundary field to study its phase transition. By continuously expanding the duration equation of the tridiagonal matrix by row and column, the eigenvalues of the local state of the matrix and the conditions for the existence of its local state are obtained. We set the right boundary field= -1.0 , so that there is no local state at the right boundary, and set the eigenvalue of the local state at the left boundary to be equal to the eigenvalue of the local state at the impurity, and then a phase transition point of the system is obtained. We find that when the left boundary field=, the boundary magnetization of the system has a sudden change, so the phase transition point is a first-order phase transition point.

Then we also calculated the magnetization at different lattice points of the system near the phase transition point through the program, and made a graph. The results show that When the left boundary field changes from the left to the right of the phase transition point, the interface of the system also suddenly moves from the left boundary to the middle point, where impurities exist. so it suddenly changes from a non-wetting phase to a partial wetting phase.

Finally, we study the finite-size scaling of the system. We first made the energy gap diagrams of different sizes near the first-order phase transition point, and then performed coordinate transformation of the energy gap images of different sizes, and It is found that after the coordinate transformation of different multiples of images of different sizes, the energy gap images of larger sizes are basically overlapped together. that is, their energy gaps satisfy the same functional relationship. Finally, we also made a graph of the relationship between the energy gap value and its size at the phase transition point of different size systems, as well as the graph of the relationship between the magnification of their abscissa and their size when we performed coordinate transformation of the energy gap images . It is found that There is an exponential function relationship between them.

In Chapter 5, we made the graph of the boundary magnetization and magnetization profiles for different combinations of values of and. Through these graphs, we understood the movement of the interface around the phase transition point for different combinations, and The effect of impurities on the interface.