Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q. 8.2 (page 333)

Draw all the diagrams, connected or disconnected, representing terms in the configuration integral with four factors of fij. You should find 11 diagrams in total, of which five are connected.

Short Answer

Expert verified

All the diagrams representing terms in configuration integral with four factors of fij have been drawn.

Step by step solution

01

Step 1. Given information

Configuration integral:- The configuration integral is used in probability theory, information theory and dynamical systems, it's a generalization of the definition of a partition function in statistical mechanics.

02

Step 2. Drawing all the diagrams representing terms in configuration integral with four factors of fij 

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

03

Step 3. All the 5 connected  diagrams are

(1)

(2)

(3)

(4)

(5)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You can estimate the size of any diagram by realizing that fr is of order 1 out to a distance of about the diameter of a molecule, andf≈0 beyond that. Hence, a three-dimensional integral of a product of f's will generally give a result that is of the order of the volume of a molecule. Estimate the sizes of all the diagrams shown explicitly in equation8.20 and explain why it was necessary to rewrite the series in exponential form.

Consider an Ising model of 100 elementary dipoles. Suppose you wish to calculate the partition function for this system, using a computer that can compute one billion terms of the partition function per second. How long must you wait for the answer?

By changing variables as in the text, express the diagram in equation 8.18 in terms of the same integral as in the equation8.31. Do the same for the last two diagrams in the first line of the equation8.20. Which diagrams cannot be written in terms of this basic integral?

In Problem 8.15 you manually computed the energy of a particular state of a 4 x 4 square lattice. Repeat that computation, but this time apply periodic boundary conditions.

Problem 8.13. Use the cluster expansion to write the total energy of a monatomic nonideal gas in terms of a sum of diagrams. Keeping only the first diagram, show that the energy is approximately
U≈32NkT+N2V·2π∫0∞r2u(r)e-βu(r)dr
Use a computer to evaluate this integral numerically, as a function of T, for the Lennard-Jones potential. Plot the temperature-dependent part of the correction term, and explain the shape of the graph physically. Discuss the correction to the heat capacity at constant volume, and compute this correction numerically for argon at room temperature and atmospheric pressure.
See all solutions

Recommended explanations on Physics Textbooks

Engineering Physics

Read Explanation

Magnetism

Read Explanation

Wave Optics

Read Explanation

Electromagnetism

Read Explanation

Nuclear Physics

Read Explanation

Physical Quantities And Units

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free