Explaining the Relation Between \gamma N_+ and 2N_{++}+N_{+-}

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In summary, The relationship between the number of nearest neighbours (\gamma) and the number of different types of pairings (N_+, N_{++}, N_{+-}) follows the equation \gamma N_+=2N_{++}+N_{+-}. This can be explained by imagining each + site being connected to its neighbors by lines, resulting in a total of \gamma*N_+ lines. This also accounts for the number of lines between different types of pairings, with 2N_{++} lines between (+,+) pairs, N_{+-} lines between (+,-) pairs, and no lines between (-,-) pairs. This relationship was first described by Kerson Huang.
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matematikuvol
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One line between (+-). Two lines between (++). Zero line between (--). [tex]\gamma[/tex] number of nearest neighbours. Why we have relation

[tex]\gamma N_+=2N_{++}+N_{+-}[/tex]

Why we get this? Some explanation. This is from Kerson Huang.
 

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Choose a + site. Join it to each neighbor by a line. we need to draw gamma lines. Now do this for all + sites. So total lines = gamma*N(+). In this process i) between any (+,+) pair there will be two lines (one when we draw line from 1st + to 2nd +, other when we draw line from 2nd + to 1st +). Now there are N(++) number of (+,+) pair. So total lines between all (+,+) pair is 2N(++).. ii) between any (+,-) pair there will be one line (when drawn from + to -). There are N(+-) number of (+,-) pair. iii) between any (-,-) pair there will be no line. So total lines = 2N(++) + N(+-).
 

1. What is the meaning of \gamma N_+?

\gamma N_+ represents the number of positively charged particles (e.g. protons) that are present in a system.

2. What does 2N_{++}+N_{+-} signify?

2N_{++}+N_{+-} represents the total number of positively charged particles that are present in a system, including both doubly charged particles (2N_{++}) and singly charged particles (N_{+-}).

3. How are \gamma N_+ and 2N_{++}+N_{+-} related?

The relation between \gamma N_+ and 2N_{++}+N_{+-} is that they both represent the number of positively charged particles in a system, with the latter including both singly and doubly charged particles.

4. What is the significance of \gamma in this relation?

\gamma represents a constant or factor that relates the number of positively charged particles to other variables in a system, such as the number of negatively charged particles or the total number of particles.

5. How is this relation used in scientific research?

This relation is commonly used in fields such as particle physics and plasma physics to study the behavior and interactions of charged particles in a system. It can also be used to make predictions and calculations about the properties and dynamics of these particles.

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