effective-java-3e-source-code | source code from the third edition | Machine Learning library

Assuming you are using Java 5 or later¹, the above code is thread-safe².

It doesn't matter that either the method or field is static provided that:

1. field being initialized is volatile and,
2. the code doing the DCL initialization is using the same mutex object for any given field.

The former is obviously true. The latter is true because all calls to getField4() are locking the same Class object.

^{1 - Prior to Java 5, the specified semantics of volatile are not sufficient to guarantee that the code is thread-safe.
2 - Thread-safe but ugly. It is better to avoid the DCL idiom and use one of the other alternatives.}

I cannot make the method static method ...

I don't see why not. It is private so you should not be constrained as to whether it is a static or instance method. It should only affect the current class.

But as noted above, it doesn't make any difference to the idiom.