In the previous few chapters of this book we have studied a variety of different Monte Carlo algorithms for simulating the using model under various conditions. In Chapter 3 we looked at the Metropolis algorithm, as it applies to the using model, and in Chapter 4 we looked at a number of other algorithms, most of which are designed to simulate the model more efficiently in the critical region, the region near the phase transition between paramagnetism and ferromagnetism. In the last chapter, we looked at a slight variation on the using model theme, the conserved-order-parameter using model, which can be used as a model of a gas, or of atoms diffusing on a surface. As we have seen, for different regimes of temperature or different variations of the model, different algorithms are appropriate. The trick is to tailor the algorithm to the type of problem we wish to tackle. However, all the algorithms we have seen so far eventually boil down to one thing: they generate a series of states, a Markov chain, in which each state is derived from the previous one in the chain, and attempt to contrive that each should appear with a probability proportional to its Boltzmann weight. In this chapter, for the first time, we will come across systems for which an approach of this kind doesn’t work. The problem, as we will see, is that for some systems, the so-called glassy systems, algorithms of this kind tend to get stuck in small regions of the state space from which they cannot escape. The reason for this is two-fold. First, the fact that each state is generated from the previous one in the chain means that there is a sense in which states are “close together”. There are states which it is easy to get to from the present one in a small number of moves, such as states which differ by the flipping of just a few spins for a single-spin-flip algorithm, and there are other states which you can only get to by making a large number of moves.
Monte Carlo Methods in Statistical Physics
Annotate
Get help with access
Get help with access
Institutional access
Access to content on Oxford Academic is often provided through institutional subscriptions and purchases. If you are a member of an institution with an active account, you may be able to access content in one of the following ways:
IP based access
Typically, access is provided across an institutional network to a range of IP addresses. This authentication occurs automatically, and it is not possible to sign out of an IP authenticated account.
Sign in through your institution
Choose this option to get remote access when outside your institution. Shibboleth/Open Athens technology is used to provide single sign-on between your institution’s website and Oxford Academic.
If your institution is not listed or you cannot sign in to your institution’s website, please contact your librarian or administrator.
Sign in with a library card
Enter your library card number to sign in. If you cannot sign in, please contact your librarian.
Society Members
Society member access to a journal is achieved in one of the following ways:
Sign in through society site
Many societies offer single sign-on between the society website and Oxford Academic. If you see ‘Sign in through society site’ in the sign in pane within a journal:
If you do not have a society account or have forgotten your username or password, please contact your society.
Sign in using a personal account
Some societies use Oxford Academic personal accounts to provide access to their members. See below.
Personal account
A personal account can be used to get email alerts, save searches, purchase content, and activate subscriptions.
Some societies use Oxford Academic personal accounts to provide access to their members.
Viewing your signed in accounts
Click the account icon in the top right to:
Signed in but can't access content
Oxford Academic is home to a wide variety of products. The institutional subscription may not cover the content that you are trying to access. If you believe you should have access to that content, please contact your librarian.
Institutional account management
For librarians and administrators, your personal account also provides access to institutional account management. Here you will find options to view and activate subscriptions, manage institutional settings and access options, access usage statistics, and more.