This paper investigates the entanglement present in the ground state of the transverse Ising model, a special case of the anisotropic XY model, which exhibits a quantum phase transition. The study focuses on the entanglement between a single site and the rest of the lattice, as well as between two sites at arbitrary temperatures and separations. The results show that the next-nearest neighbour entanglement is maximized at the critical point of the phase transition, while the nearest-neighbour entanglement is not. The critical point in the transverse Ising model corresponds to a transition in the entanglement between a single site and the rest of the lattice. The paper discusses the quantum phase transition (QPT) in the XY model, which is a qualitative change in the ground state of a quantum many-body system as a parameter is varied. Unlike ordinary phase transitions, which occur at nonzero temperatures, QPTs are fully quantum and involve long-range correlations in the ground state. The paper argues that the property responsible for these long-range correlations is entanglement, and that the ground state of the system is strongly entangled at the critical point. The study uses the Jordan-Wigner transform to solve the XY model exactly and calculate the two-site reduced density matrix for all pairs of sites. From this, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. The results show that the entanglement between a single site and the rest of the lattice is maximized at the critical point, and that the next-nearest neighbour entanglement is also maximized at the critical point. The paper also discusses the role of entanglement in the quantum phase transition of the transverse Ising model. It shows that the critical point corresponds to a transition in the entanglement between a single site and the rest of the lattice. The study uses the concurrence measure to quantify the two-party entanglement between two sites in the ground state of the transverse Ising model. The results show that the entanglement between neighbouring sites and next-nearest neighbour sites is maximized at the critical point, while all other pairs have zero two-party entanglement. The paper concludes that the entanglement present in the ground state of the transverse Ising model is maximized at the critical point, and that the next-nearest neighbour entanglement is a key feature of the quantum phase transition. The study also highlights the importance of entanglement in understanding complex quantum systems and the potential for using entanglement measures to study the universal properties of critical quantum systems.This paper investigates the entanglement present in the ground state of the transverse Ising model, a special case of the anisotropic XY model, which exhibits a quantum phase transition. The study focuses on the entanglement between a single site and the rest of the lattice, as well as between two sites at arbitrary temperatures and separations. The results show that the next-nearest neighbour entanglement is maximized at the critical point of the phase transition, while the nearest-neighbour entanglement is not. The critical point in the transverse Ising model corresponds to a transition in the entanglement between a single site and the rest of the lattice. The paper discusses the quantum phase transition (QPT) in the XY model, which is a qualitative change in the ground state of a quantum many-body system as a parameter is varied. Unlike ordinary phase transitions, which occur at nonzero temperatures, QPTs are fully quantum and involve long-range correlations in the ground state. The paper argues that the property responsible for these long-range correlations is entanglement, and that the ground state of the system is strongly entangled at the critical point. The study uses the Jordan-Wigner transform to solve the XY model exactly and calculate the two-site reduced density matrix for all pairs of sites. From this, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. The results show that the entanglement between a single site and the rest of the lattice is maximized at the critical point, and that the next-nearest neighbour entanglement is also maximized at the critical point. The paper also discusses the role of entanglement in the quantum phase transition of the transverse Ising model. It shows that the critical point corresponds to a transition in the entanglement between a single site and the rest of the lattice. The study uses the concurrence measure to quantify the two-party entanglement between two sites in the ground state of the transverse Ising model. The results show that the entanglement between neighbouring sites and next-nearest neighbour sites is maximized at the critical point, while all other pairs have zero two-party entanglement. The paper concludes that the entanglement present in the ground state of the transverse Ising model is maximized at the critical point, and that the next-nearest neighbour entanglement is a key feature of the quantum phase transition. The study also highlights the importance of entanglement in understanding complex quantum systems and the potential for using entanglement measures to study the universal properties of critical quantum systems.