# Tag Info

## Hot answers tagged spin-chains

15

Arnold Neumaier's comment about statistical mechanics is correct, but here's how you can prove it using just thermodynamics. Let's imagine two bodies at different temperatures in contact with one another. Let's say that body 1 transfers a small amount of heat $Q$ to body 2. Body 1's entropy changes by $-Q/T_1$, and body 2's entropy changes by $Q/T_2$, so ...

12

From a fundamental (i.e., statistical mechanics) point of view, the physically relevant parameter is coldness = inverse temperature $\beta=1/k_BT$. This changes continuously. If it passes from a positive value through zero to a negative value, the temperature changes from very large positive to infinite (with indefinite sign) to very large negative. ...

2

To expand on LubošMotl's comment, see the following classic paper by Lieb, Schultz and Mattis. For one-dimensional systems and nearest neighbor interactions, the spin chain that you mention as an example in the comment can be converted into a free fermionic model. See section II in the above paper for details.

1

Take a hydrogen gas in a magnetic field. The nuclei can be aligned with the field, low energy, or against it, high energy. At low temperature most of the nuclei are aligned with the field and no matter how much I heat the gas I can never make the population of the higher energy state exceed the lower energy state. All I can do is make them almost equal, as ...

1

There are plenty, the condition is very weak. For a simple example, with N spin 1/2, all spins up and all spins down both have total angular momentum N/2. You can make a Hamiltonian be zero on the N/2 total angular momentum states, so that all N/2 states are eigenstates, but it can be anything at all to the states of lower total angular momentum, without ...

1

XX (and more generally XY) spin models became very popular lately, especially in connection to quantum-information theoretic problems. The XY model (without magnetic field though) has been introduced and properly solved in 1961 by Lieb, Schultz and Mattis (Ann. Phys. 16, 407, (1961)). By the way this is a great reference to start with, if you didn't read ...

1

Wick's theorem works for an arbitrary number of states equipped with their creation and annihilation oscillators. In the same way, Wick's theorem for spins applies to a collection of an arbitrary number of spins - or qubits, which is the same thing if their spin is $1/2$. Wick's theorem is just a mathematical identity that works even for - and especially for ...

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