Is unsynchronized read of integer threadsafe in java?

No, it's not threadsafe. invoc needs to be declared volatile, or accessed while synchronizing on the same lock, or changed to use AtomicInteger. Just using the synchronized method to increment invoc, but not synchronizing to read it, isn't good enough.

The JVM does a lot of optimizations, including CPU-specific caching and instruction reordering. It uses the volatile keyword and locking to decide when it can optimize freely and when it has to have an up-to-date value available for other threads to read. So when the reader doesn't use the lock the JVM can't know not to give it a stale value.

This quote from Java Concurrency in Practice (section 3.1.3) discusses how both writes and reads need to be synchronized:

Intrinsic locking can be used to guarantee that one thread sees the effects of another in a predictable manner, as illustrated by Figure 3.1. When thread A executes a synchronized block, and subsequently thread B enters a synchronized block guarded by the same lock, the values of variables that were visible to A prior to releasing the lock are guaranteed to be visible to B upon acquiring the lock. In other words, everything A did in or prior to a synchronized block is visible to B when it executes a synchronized block guarded by the same lock. Without synchronization, there is no such guarantee.

The next section (3.1.4) covers using volatile:

The Java language also provides an alternative, weaker form of synchronization, volatile variables, to ensure that updates to a variable are propagated predictably to other threads. When a field is declared volatile, the compiler and runtime are put on notice that this variable is shared and that operations on it should not be reordered with other memory operations. Volatile variables are not cached in registers or in caches where they are hidden from other processors, so a read of a volatile variable always returns the most recent write by any thread.

Back when we all had single-CPU machines on our desktops we'd write code and never have a problem until it ran on a multiprocessor box, usually in production. Some of the factors that give rise to the visiblity problems, things like CPU-local caches and instruction reordering, are things you would expect from any multiprocessor machine. Elimination of apparently unneeded instructions could happen for any machine, though. There's nothing forcing the JVM to ever make the reader see the up-to-date value of the variable, you're at the mercy of the JVM implementors. So it seems to me this code would not be a good bet for any CPU architecture.

Well!

  private volatile int invoc = 0;

Will do the trick.

And see Are java primitive ints atomic by design or by accident? which sites some of the relevant java definitions. Apparently int is fine, but double & long might not be.

edit, add-on. The question asks, "see the correct value of invoc ?". What is "the correct value"? As in the timespace continuum, simultaneity doesn't really exist between threads. One of the above posts notes that the value will eventually get flushed, and the other thread will get it. Is the code "thread safe"? I would say "yes", because it won't "misbehave" based on the vagaries of sequencing, in this case.

Theoretically, it is possible that the read is cached. Nothing in Java memory model prevents that.

Practically, that is extremely unlikely to happen (in your particular example). The question is, whether JVM can optimize across a method call.

read #1method();read #2

For JVM to reason that read#2 can reuse the result of read#1 (which can be stored in a CPU register), it must know for sure that method() contains no synchronization actions. This is generally impossible - unless, method() is inlined, and JVM can see from the flatted code that there's no sync/volatile or other synchronization actions between read#1 and read#2; then it can safely eliminate read#2.

Now in your example, the method is Thread.sleep(). One way to implement it is to busy loop for certain times, depending on CPU frequency. Then JVM may inline it, and then eliminate read#2.

But of course such implementation of sleep() is unrealistic. It is usually implemented as a native method that calls OS kernel. The question is, can JVM optimize across such a native method.

Even if JVM has knowledge of internal workings of some native methods, therefore can optimize across them, it's improbable that sleep() is treated that way. sleep(1ms) takes millions of CPU cycles to return, there is really no point optimizing around it to save a few reads.

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This discussion reveals the biggest problem of data races - it takes too much effort to reason about it. A program is not necessarily wrong, if it is not "correctly synchronized", however to prove it's not wrong is not an easy task. Life is much simpler, if a program is correctly synchronized and contains no data race.