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This paper traces the military role of Tibnīn and its rulers in the Latin East against the Muslims until 1187/ 583. Tibnīn played a key role in overcoming the Muslims in Tyre and controlled it in 1124. It also played a vital role in the conflict between Damascus and the Kingdom of Jerusalem. Tibnīn participated in defending Antioch, Banyas, Hebron and Transjordan several times. Furthermore, its soldiers and Knights joined the army of the Kingdom of Jerusalem to capture Ascalon in 1153, and joined the campaigns of Amaury I, King of Jerusalem, against Egypt from 1164 to1169. The military situation of Tibnīn under the rule of the royal house until its fall to the Muslims in 1187/ 583 will be studied as well
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density